So the next paper is by Mark Oliver Poller from Hyderabad Institute for Triagra Studies and it's about testing quantile forecast optimality. As usual you have 25 minutes and then 10 minutes for discussion and 10 minutes for Q&A. Yeah, thanks a lot to the organisers for you're organising this nice conference and in particular for having our projects on the menu and in general for also including papers on forecast evaluation. I mean in the poster session we already had two nice posters on forecast evaluation and this is also a talk on forecast evaluation and this is joint work with Jack Foster from Kings College, London and Daniel Gutknecht from Goethe University, Frankfurt. Yeah, so it's title testing quantile forecast optimality and the motivation is of course quantile forecasts are becoming more and more popular. I don't need to tell you that anymore and in economics and finance they come in the forms of growth at risk, inflation at risk, value at risk and our goal is to evaluate quantile forecasts and we are in particular focusing on evaluating the forecast over multiple horizons because in practice usually we do not forecast only for one quarter into the future but for many quarters and we ideally want to evaluate our full forecasting approach not only a forecast for a single horizon. Okay, so this is what we focus on multiple horizons and then as we've seen for example in the previous talk often also not only a single quantile is of interest but multiple quantiles. Let's say if we have prediction intervals or if we want to approximate the full distribution by a set of quantiles then we are in a multiple quantile situation. Okay, so this is a paper about multi-horizon, multi-quantile forecast evaluation and then usually forecast evaluation can be divided into two classes of approaches. The first one is relative evaluation where you compare different forecasting approaches that we have seen a lot today. Yeah, compare these approaches by an expected loss let's say expected quantile score. This is not what we are doing we are interested in absolute forecast evaluation where you have a single forecasting approach and you want to check if this approach is in line with the data or if the forecaster uses information efficiently. Okay, and why should you be interested in absolute evaluation? I mean clearly in a horse race your best fanciest model yeah can read all other models but also the best model can be very bad and so you should always, at least I say that, you should always complement your relative evaluation with an absolute evaluation where you test at the model or the forecast for some basic properties which we usually call optimality, efficiency or calibration depending on the literature that you come from. Okay, and this is what we do. We, that's the delay. We propose an optimality test, several optimality tests for multi horizon and multi quantile forecasts. A little bit on the literature, I mean there's a huge literature on optimality testing for quantile forecasts at least in the single horizon single quantile case. Yeah, some papers I listed here but there are many, many more and then in relative when it came to relative comes to relative evaluation one of the organizers of this conference forcefully argued that I mean in the case of mean forecasts but in particular in general for relative evaluation you should evaluate over all forecast horizons jointly and not just consider a single forecast horizon for evaluation or consider all the single horizons and do a test on them separately but do a joint test and we try to do the same thing in the quantile case for absolute evaluation. Okay, what do we do? We pick a specific notion of optimality which is called, has been called auto calibration in the literature. This may be not such a familiar term but this is essentially the notion that a Minzer-Sanowitz regression tests or in our case a quanti Minzer-Sanowitz regression and we built on those Minzer-Sanowitz regressions to test this notion of auto calibration. We allow as I said for multi horizon and multi quantile forecasts. Our tests are based on a set, a finite set of moment equalities and we use bootstrap critical values and we also have some extensions. You can also test stronger forms of optimality or calibrations while augmented Minzer-Sanowitz quanti regressions and a multivariate version for example to test the forecast from the from the previous talk. You can also test quanti forecasts for multiple for multiple variables at the same time. Okay, so we provide some simulations of course to analyze the finite sample performance and we have a macro and a finance application so a value at risk and a growth at risk application to showcase how our tests may help you in practice to evaluate your models. Okay, let me start by introducing our basic tests and before that let's look at the setup. So the goal is of course to forecast a certain quantile or multiple quantiles but let's start with a single quantile. So our variable of interest we call yt let's say it's inflation. The target period is called t and we are we are standing h, h periods in the past let's say that's the forecast horizon h and we try to forecast a certain quantile yeah the 5% quantile so it's for example the tau quantile of yt given the information that we have in t-h. Okay, so this f t-h is the forecast this information set. Okay and then we denote this quantile forecast by y hat and tau is the quantile level, t is the the target period and h is the forecast horizon. Okay and now we are in this multi-horizon multi-quantile setup so we have forecasts for possibly many horizons from 1 to capital H and for possibly k capital K different quantile levels. Okay, what is basically our null hypothesis or what do we want to test? So we call a quantile forecast is called optimal with respect to the forecast as full information set if it's equal to the true conditional quantile of yt given the information set. This notion of full optimality is usually hard to test because we don't know the information set of the forecaster and it's usually large. So what we test in our main test is the notion of auto calibration. Here the full information set of the forecaster is replaced basically by the forecast. So we condition on the information that we have in the forecast. Okay, so this is the notion that a that a mean sartanowitz or a quantile mean sartanowitz regression tests optimality with respect to the information contained in the forecast. So you can interpret this as your forecast you should take them at face value. You should not apply some transformation to them. If they are too calibrated you should take them as they are. Okay, this is a weaker notion of optimality but it's also an important property of of the forecasts itself. Okay, so and what do we do to test this? So we use some quantile mean sartanowitz regressions. They were first introduced in this Galliano net at all paper in the quantile case. So what what you do is very simple. You take your evaluation sample you take the observation the realization for YT and you regress it on the forecast. Okay and then if we go to the previous slide the mean sartanowitz or the regression line models or estimates this conditional quantile here and under auto calibration you see the regression line should be equal to the forecast. So auto calibration implies the intercept should be zero the slope should be equal to one. So this is then essentially what we formulate as our null hypothesis. Yeah for for all horizons that we have for all quantile levels you run these regressions. We have these population regressions and the null hypothesis is intercepts are zero, slopes are equal to one. Yeah and rejecting the null then implies systematic errors in the forecast, a violation of this hypothesis of auto calibration. And in the end our test gives you of course a single test decision over your whole forecasting approach but we can also zoom in as we'll see in the applications and see how we can possibly improve our forecast. And then the first way that we can zoom in is we can look at the contributions of single quantiles or horizons or quantile horizon combinations to our test statistic to see where do the problems lie is it further into the future when you forecast further into the future or is it at alter quantiles. And we can also look at the estimated means sartanowitz regression lines to get an idea in which direction we should try to try to improve our forecast. We'll see that in the applications. Okay so we have an evaluation sample of forecasts in the end. So the evaluation sample has size p as standard in the literature this notation I guess. And we have a matrix valued so that the forecast are matrix valued because we have we have these multiple horizons we have these multiple quantiles. Yeah so in the end we have the forecast and the realizations and we run although we estimate all those quantile regressions the min sartanowitz quantile regressions save the coefficients that we estimated and then the test statistic just takes the deviation of the estimated coefficients from their values under the null. Okay so estimated intercept minus zero so the estimated intercept and estimated slope minus minus one under the null and these are the empirical moments that we use these m hats and then we basically just sum them up scale them up by the evaluation sample size and square them and this is the test statistic you so you can interpret this test statistic as a basically summing up the distance from all those from the regression lines under the null to the to the estimated regression lines. Okay so the asymptotic distribution of this thing here of course depends on the variance covariance matrix so on the dependence between all those estimated coefficients and we do not estimate the variance covariance matrix we use a bootstrap implementation so a moving block bootstrap yeah and we take the critical values from this moving block bootstrap and we establish the validity of course of this bootstrap under certain assumptions in particular we assume that the evaluation sample and the estimation sample if we have if you have an estimated model that they both go to infinity but the estimation sample dominates the the evaluation sample. Okay so this is our basic testing procedure yeah let's shortly look at at the two extensions that we that we also provide. Okay so I mean you can also try to test stronger forms of optimality where you do not only evaluate the forecast conditional on on the information contained in themselves but yeah in principle you could test full optimality so with respect to the full information set but then you would have to include all the variables from the full information set into the regression so you can then run augmented Minzat-Sahnowitz regression where you if you think that some variable is important for forecasting the other variable then you can check if this variable z or this vector of variable z if the information from this was incorporated efficiently. Okay so this would then be a stronger form of calibration or optimality and here the null would be the same as before but the coefficients on these additional variables should be zero because the forecasts on the right hand side under the null already efficiently incorporate all the information. Okay and rejecting this null would mean that the additional variables contain additional information which which are useful in forecasting and should be incorporated into into your models. Okay and the other extension is yeah if you just have multiple variables and quantile forecasts for them you our approach extends straightforwardly in that direction. Okay then let's look at the two empirical applications the first one is a value-at-risk application from finance this is more about the basic test application of the basic test and the second application is is a macro application which is multi-variates and where we also apply the the other extension of the augmented Minzat-Sahnowitz regression. Okay I mean in financial risk management value-at-risk is of course important and usually yeah you want to you have a single level for value-at-risk but there's no real consensus which is the right level 1% 2.5% or 5% let's say and more modern risk measures like expected shortfall basically look at the look at the information in the in the full tail so yeah you could be interested in multiple quantiles let's say but you're definitely interested in multi horizons when you do risk management you're not only interested in in risk management for the next day so our approach is naturally suited to this to this financial risk management setup and we use in our application daily S&P 500 returns with a standard GARCH 1.1 model as we had that several times today we generate the multi-step they had quantile predictions by the SCARCH bootstrap by Pascal et al that's basically resampling from from your estimated residuals to to simulate forward from the model and then take the empirical quantize from that the data span from 2000 to 2022 and we use the recursive window of initial estimation size 3000 we go up to 10 horizons so from horizon 1 to 10 over all those horizons we forecast and we take those three quantile levels here 1, 2.5 and 5% as a block length for the bootstrap we use 10 and yeah we do some robustness checks which do not really really change the results qualitatively so here there's just a picture of the realizations and those three quantile forecasts for the first horizon remember we we do go up to 10 horizons and I mean this is the output of our test so we have a test statistic a value of the test statistic the the bootstrap critical values and here's the bootstrap p value so it's 1% so the test gives us a decision our model there's strong evidence that that this risk manager risk management forecasting model is not auto calibrated okay that's the overall decision that's what we wanted but of course we can now zoom in and look at the contributions to the test statistic from single horizon quantile combinations yeah see the inside the table or from single from a single quantile down here or from a single horizon and if you look for a longer time at this you will see that for the outer quantiles the the deviations from the null are larger so 5% of predictions seem to be okay from the scotch model for the outer quantiles it gets a bit more the test statistic gets larger or a lot of contributions and for the the smaller horizons what h being equal to one or two there is not so much evidence and against auto calibration as for the for the larger horizons thanks okay um what you can also do you can look at individual p values that you that you get with our tests only testing single horizon quantile combinations or single contents or horizons we have that here the the individual p values but why do I show that and I showed it to you to to to make clear what you would have if you didn't have a joint test you would have all those individual p values and you would have to combine them so this is what what's the a major benefit of our approach you have this this overall testing decision the p value of one percent and you do not need to find a way to combine all those p values or this is the way that that we give you okay one more way to zoom in as I promised you you can look at individual i'm in sartano its regression lines because you have estimated them so for a specific horizon and specific quantile let's say for those cases that contributes most strongly to the rejection um so here is a scatterplot of forecasts and realizations um and the orange line is the diagonal so here we have the um the forecast for the one percent quantile this is and for for h being equal to one so here we have the forecast on the diagonal essentially the one percent quantile forecast if the area and the the min sartano its regression line gives you the auto-calibrated forecasts so the how where the forecast should have been if they if they were to be auto-calibrated and then you can can see yeah for example um here in the more extreme cases um we are too conservative the the the quantile forecasts are too low they they wouldn't need to be so low of course this is the linear this is the linear regression you could do that um non-parametrically um but this is not the focus here but you can get some idea on how you should improve your quantile forecasts um by looking at those regression lines okay to finish off um let's look at the macro application um yeah i don't need to give you a motivation on quantile forecasting and macro um we explore optimality of model-based forecasts of four us macro variables the same variables as in man san 2015 who was one of the first probably to to consider quantile forecasting in macro um and we use monthly not quarterly variables and we look at um two inflation variables the first one here and the last one and industrial production and employment so two real variables and um we use the classical quantile autoregressive distributed lack model by by or not by abg but that they also use we regress those variables on an autoregressive term and on the national financial conditions index of the chicago fed um we use the threat monthly data um from 1984 on um we have 432 observations we split the sample in half um for the initial estimation sample and we go up to 12 horizons into the future so one year 12 months and we use the 10 percent quantile 25 and percent quantile and the median here the block length for the block boot swap is four um and now let's look at this um this multivariate version of the test so jointly the quantile forecasts for all the quantiles of all the horizons for all the variables we get a p-value of about seven percent so there's some evidence that not all those forecasts are auto-calibrated and then we can also look at the individual series and here we see interestingly that the two real variables industrial production and um employment there is not not really evidence against auto-calibration p-values are larger than 10 percent for the two inflation variables there is more more evidence with a p-value of essentially 10 percent and zero more evidence for for miscalibration so one take away could be the abg approach for gdp growth yeah is is more or less okay because it's about the real variable but for the inflation variables inflation at risk maybe you should you should look for a different model um okay um i mean you could also zoom in like we did for the other application we don't do that now um let's look at the other extension the augmented minstrel zhanowitz test where we check if here here we check if one of the other variables um contains useful information um because we just include the three other variables um in the augmented minstrel zhanowitz regression and then of course the um the inflation variables got a rejection for the v-canal hypothesis for auto-calibration they still get a rejection but for the real variables yeah we don't get a rejection the other variables do not seem to carry important information um about um yeah the the two real variables here so no improvement of the forecast possible via including the other um variables in the model okay great so um what we did we proposed a minstrel zhanowitz type test for quantile forecast optimality at multiple horizons and multiple quantile levels which we think is yeah practically very relevant we provided those two extensions or a stronger form of auto of calibration for the widely augmented minstrel zhanowitz test and the extension to multiple time series um yeah simulation evidence that i didn't show you today shows that um the tests work well in in finite samples and we have yeah these two large empirical applications to illustrate the the usefulness of the tests yeah thanks a lot for your attention i'm looking forward to the discussion thank you mark the discussant is laura coronel from the university of york that's been really a pleasure sorry to to read the paper and uh i'm gonna just start with um just small introduction um saying what the paper does so this is a test essentially for misspecification for multiple quantile forecast at multiple multiple forecasting horizon and what the paper does is that it builds on multiple minstrel zhanowitz quantile regressions cast in a moment equality framework so um essentially um when we do in general forecast evaluation uh in the case of point forecast we do forecast evaluation um horizon by horizon so or we are in a quantile type of forecast we do quantile by quantile what this paper does is that it proposes a procedure that we can test uh for uh um specification we can do specification test uh jointly for all the quantiles at all the forecasting uh horizons and the main test is for this null hypothesis of auto calibration which is optimality with respect to the information contained into the uh forecast themselves but it also proposes two extensions one is the extension uh for optimality with respect to larger information sets so with documented uh means quantile minstrel zhanowitz regression and the other one which i think is more interesting and more relevant for the work we've seen in this um um this workshop is for auto calibration for multiple series uh so if we have a model that provides us forecast for multiple series each it's different forecasting horizons and for different quantiles so what they're proposing is a test that allows us to test for the specification of the model jointly for all the series for all the quantiles and for all the forecasting horizons so i'm very enthusiastic about this paper uh so uh let me uh go a bit into the uh the definition of uh auto calibration it is uh used so here uh we have that uh soy forecast which is indicated by y hat at for the variable at time t um made each period ahead and for quantile tau is auto calibrated if it is equal to the conditional quantile of the variable at y t conditional the information set that was used to uh to make the forecast that is contained into the forecast itself so what the paper proposes is to use these quantile minstrel zhanowitz regressions which means essentially that it regresses the um it does a quantile regression of the variable of interest essentially y t on the forecast and if the forecast is auto calibrated what you should have is that alpha so the intercept should be zero and beta should be one for all the quantiles and for all the forecasting horizons so this is the null hypothesis of the test so the null hypothesis is a joint hypothesis that all the alphas and all the beta so all the alphas are equal to zero and all the betas are equal to one for all the quantiles and all the forecasting horizons the alternative hypothesis is that at least one alpha or one beta are different than zero for some forecasting horizons or conditional quant or sorry or um quantile yes so um since um the paper uses these uh quantile minstrel zhanowitz test is natural to estimate alpha and beta using quantile regression so this is what the paper essentially does so once you estimate the alpha and betas in quantile regression so the paper says okay um here we have that this is what we get our estimate and this is what we have under the null hypothesis right so the alphas should all be equal to zero and the betas should all be equal to one so these are what are the moment conditions that we have essentially and they have this distribution so if you want to do a world test what you would have to do is essentially to construct a test statistic that normalizes for this variance what they say is that this can be um so this uh the dimensionality of the problem can become big if you have many quantiles and many forecasting horizons and even more if you want to go multivariate so let's go the other way around so what they do is that they propose essentially to sum up all the elements in these moment conditions so all these here to square them so first to square them and then to sum them all up okay so this distribution this test statistic sorry this is the test statistic where did it go sorry here so this this statistic is non-pivotal because we didn't we don't have we didn't normalize for the variance right so we need to compute critical values using bootstrap so what they use I didn't go too much into the details in the presentation but they use moving block bootstrap directly from the forecast and then of course it's assumed that the estimation sample is large enough and that's the estimation error is irrelevant um and then um as uh Mark said they propose two extensions one is the augmented quantile means exam which in which essentially the test efficiency with respect to a larger information set by adding additional regressors into the quantile regression and adding the hypothesis that the coefficients on these additional regressors should be zero and then the multivariate one that is for multiple variables okay so my comments general comment is that this is very interesting paper and addresses are important issues that is very relevant for whoever has to make decisions about which forecast to use which model you select so I think that this is the best place to present this paper and as I already said when you have multiple forecasting horizons multiple quantiles then the dimensionality of the problem can become big very easily and especially if you go multivariate so a wall test is not feasible so I think that they they got around the problem in a very smart way proposing a feasible test statistic that has uh good properties uh I have essentially uh three comments so the first one is about bootstrap then the Monte Carlo which was not into the presentation and then on the pick application first uh this is I don't know if it's a comment or a clarification but this was the same also in the presentation so reading the paper is not clear to me how the bootstrap is implemented because in the auto calibration test you say that you bootstrap example jointly the observation and the quantile for each tau so which I think that you do multiple times while instead in the multivariate extension it looks that you take them jointly so my view would be that they should always be taken jointly so you should the example jointly always all the quantiles and all the forecasting horizons so I don't know if this was just how it was written or how you're doing it so it's a question and second uh in the paper they're not um the the the the bootstrap is described for the case of auto calibration but then uh it's skipped a bit in the other two extensions but in the case where you have uh the augmented means are done with regression maybe you could specify also how you treat the conditioning variables do do you resample them or do you keep them as fixed um so this is about the bootstrap and then I think my main comments are about the the Monte Carlo simulations so I think there is lots of scope to expand the Monte Carlo in the paper because it is quite uh tiny and it's good to have new tools but you know a new tool is not like a new game you want to see how much it works when it works and which are the rules of the game somehow right so now the the Monte Carlo that we have in the paper looks at let's say two sample sizes and three choices for the block selection in the block bootstrap but for example the auto correlation coefficient the data generating process is fixed 2.6 so how has this number been chosen and maybe you know the final sample size depends on this uh and this auto correlation so it would be interesting to see how like the properties of the test change if you have different auto correlation in in the data generating process and then also for when you look at the sites of course you use the correct um auto regressive coefficient when you use a power you use a larger so 0.8 auto correlation but it would be interesting to explore how uh the power of the test depends on the deviation so um so how wrong you are from you know the null hypothesis uh then um uh or the data generating process so how does the power depend on this deviation and maybe if the power depends also on the auto correlation of the process um and then um also uh there are three choices of block selection but then these are used in the Monte Carlo but for the empirical application um for one the one with the financial data the the value at risk the block it is chosen is not included in the Monte Carlo so and my use that's most likely the block depends on the auto correlation so coefficient so maybe this is something could be also be explored um and then point two which i think is relevant so it's um interesting approach that allows you to test lots of moment conditions i would be interesting to know how far we can go so now in the Monte Carlo you have three quantile levels and four uh horizons so like 12 moment conditions when does the test break right so so can we go up to 20 to 50 100 so this is also interesting to know especially for whoever wants to apply the test and then uh since we are in a central bank we deal with macro data the smallest sample size in the um in the Monte Carlo is 120 so you know with quarterly data indeed in your um um application in macro you use monthly data right but if you want to use quarterly data 120 is a lot so what happens if you have smaller sample sizes uh and then my final comment is the in the big application so i like a lot this idea of recalibrating the forecast and i think this could be explored a bit more in the paper uh so to look how this recalibrated forecast what they look like and how you could combine the recalibration that you do for different quantiles at different forecasting horizons um and then since i think i'm almost out of time these are minor points i can tell you later uh i want just to say that this is a very interesting paper um that addresses a very important issue and proposes three tests one for autocalibration one for optimality with respect to larger information set and auto calibration for multiple series and to conclude i want to say that the paper has a hidden gem in the appendix which is the horizon monotonicity test which i find very interesting and is a bit um frustrating for it to be in the appendix so i was wondering if you could maybe put it aside in another paper and do Monte Carlo and then bigger application because i found that's very interesting uh i know that appendices they um they evolve with the paper so i wonder why is in the appendix um should i say again jump out of the ccb uh uh no very nice presentation many thanks actually i was now inspired also by one poster that it was outside which was about combination of the quantiles and we are always struggling as you said you know how to combine models and what horizon within one or two years so is this just a direct application that we can do that have you thought about combination of you know quantile models using this information because now you can combine with an optimality you know with a function with optimizes over horizons right for example thank you julian manto on bank of england um i have a couple of questions the first one is um i don't know if i missed the point about how do do your tests solve the problem of multipolypothesis testing especially in the multi-horizon dimension uh and then i was wondering whether it makes a difference how you compute the horizon the the forecast horizon so if it's a direct forecast or indirect forecast if you see any difference i guess no but let you answer thank you thank you points thank you for the clear presentation uh to me the the test is a bit non-constructive so if uh if the test rejects then uh then that's too bad for the modular but to me it's there's no no guidance on which which part of the specification i should now change for the for the test to uh to to to indicate a good model specification and one way to perhaps be more constructive is for me to know whether the test just rejected because the alphas are not are not zero or whether the test rejected because the slope coefficients are not equal to one so person can disentangle the test statistic and then i would know why the test rejected thank you um so pushing on this and the point was made by Juan um indeed it would be interesting to have a way instead of a testing model in a way to combine different quantile estimates and then you also solve this issue you know she said the perspective that any model is mis-specified then this could be one way to aggregate different uh forecasts and i guess it's linked to the poster session that uh seen before and another question on on time horizon there are many ways to look at the time horizon one is to look from t from t minus h to t but it can also do uh you know each step at a time there may be although they're not um you cannot sum them but they can be value right and seeing whether the model is doing a good job also estimating from t minus two to t minus three and so forth all these small steps forecasting steps instead of just doing one direct quest okay um yeah thanks a lot Laura for this very nice discussion and thanks for all your questions and comments um i'll try to answer um most of them um so the first question was uh on the on the joint resampling um yeah i think this is not written clearly in the paper we jointly resample the observation and the whole matrix of forecasts um so then um okay and the resampling of the of the additional regressors and the mental standards of augmented regressions this was a bit complicated um i would have to to check to check how we did that um yeah but it's not yeah yeah it's not it should be extended in the paper probably the description of that um yeah i mean all the the comments on the simulations um yeah i take with me and this could be well discussed and with my co-authors yeah definitely they are um they are a bit brief the simulations but actually for submission we we put all of them in the appendix so um yeah but they could they could be extended definitely um yeah and this is also what the referees remarked um but something that you said um for the we have a a simulation that is more tailored to the macro application not to the finance application and yeah we will have more simulations which are which are from a garage model um um we we chose the block length for the bootstrap there um longer because the time series is just longer for the for the for the financial series and the the dependence is probably stronger than in the macro case um but we'll have simulations backing that up um okay then um yeah two two very interesting comments the two last ones um so on the recalibration um maybe i'll explain that shortly so the mental turnovers regression line we've seen one picture it gives you it in a way tells you how the forecast should have looked like if they were auto calibrated because it estimates the auto calibrated forecast from the actual forecast and this is then in the literature um for me in forecast or in in other literatures like the meteorological one it's called recalibration so taking forecasts and manipulating them in a way that they that they come better um let's say um yeah we are thinking of a follow about the follow up project where we take your forecast from structural economic models like dsge models and try to recalibrate them because they are interpretable but maybe the forecast accuracy is not as as good as for statistical models yeah for statistical models yeah i'm not sure if this this leads to much improvement and then you also have the problems of gradual structural change and well the coefficients that you estimate based on the past really helps you to recalibrate your current forecast yeah but that's certainly something interesting that we that we look into um yeah and then we also have this horizon monotonicity test and the appendix that i didn't mention thanks for mentioning it so this is essentially also a test for optimality which i mean we have this quantile score we have seen this a lot today and the expected quantile score should um should increase over the horizons because the forecast accuracy should get should get worse the further into the future your forecast because you just should have less information um about 10 10 periods into the future than about tomorrow let's say um and we we just propose a test for it we have a test for that which is from a technical point of view maybe more involved than this one um but yeah usually when you look at forecasts in practice the um the loss is increasing over the horizon so sometimes you have a non-monotonicity there but that's probably noise so we we didn't really find suitable applications for that test so we we put it into the appendix um yeah okay then um the question on quantile combination or combination of quantile forecast yeah probably should ask julia i'm not an expert on that really but yeah you could use this let's say augmented mental sandwich approach and regress run a regression of of your variable on on different quantile uh forecasts and this this would give you a linear combination of them but i'm sure someone has tried that already i don't have a reference but that's probably the simplest thing i don't know yeah but yeah i'm not too too much into that literature um so then uh your question was uh how how we we solved the multiple testing problem um i mean in the end we give you one p value and if you had a test for every single horizon every single quantile you had many p values and you would have to combine them and the bonferroni correction or something like that we know that it's you lose a lot of power basically doing that so here we we don't lose lose power i would say that's yeah that's and maybe the main contribution um that we that we solved this problem um then i didn't really get it there's no difference if the depending on so if the forecast the direct or indirect this this doesn't this doesn't matter for our test we take the forecast as as primitives as as we see so we don't we don't go the it doesn't matter from where they come let's say we we take just just the forecasts we take them as given um okay so then um yeah the comment that the test is non-constructive um it's essentially yeah we have a p value in the end which tells you nothing so it gives you a decision uh on a statistic problem or a decision problem as you want but um yeah then i i tried to show in the applications that we can zoom in in a way and look at the test statistic is nicely interpretable in a distance kind of way and you can look at the contributions of different horizons or quantites or combinations of them i mean this this can give you a flavor of of where something goes wrong um maybe at every horizon and quantile you have a have a problem okay but yeah this can give you a flavor and then um yeah as you said you can look at the single in sartanowitz regressions and you can look at the coefficients or you can even plot the regression lines and see um see what is going so how it deviates from the from the diagonal um wanted to do that i would use a non-parametric approach on that that's done in the statistical or meteorological literature um so there's this scatter plot of observations and and forecasts and and then you estimate this regression line non-parametric field and sartanowitz regression line that's called a reliability diagram or calibration plot in the in this literature it's it's a fairly new tool for quantile regression i would say but you could you could always do that um and then see um um what is what is tells you where your forecast could be improved and wouldn't take the linear regression line literally as i said because it's only a linear regression and we have structural change and so on but you could get some some um ideas on how to improve your forecast um yeah um yeah this was your your first question i guess and i would have to think about the the second one so um so the gradual the gradual forecasting um might also be interesting to think about how to evaluate them well thank you thank you lot mark and thanks to all the speakers


How would you grade the coalition policies on the issue of a federal ICAC? Look, I'm very disappointed by the government's position on a federal ICAC and I've given them an F a fail. I would rank it as a fail. I've graded the coalition's policy as an E. At an E on the A to F scale. I give them a grade of E, better than nothing, but only just. Details of what the coalition's put forward would be worse than having nothing. Effectively, it would be set up to give the appearance of a federal anti-corruption commission, but not actually be able to do the full job that we expected to. I'm also deeply, deeply concerned by the 2020 draft bill, a almost complete lack of commitment to pursuing this reform as a matter of urgency or even as a matter of priority for the government. The proposed model is very watered down and weak. There are many deficiencies in the bill. There's a number of shortfalls, narrow definitions of corruption. The coalition's model also has a narrow focus on criminal conduct. It defines corruption very, very narrowly. The bar for investigation is too high, requiring a suspicion of criminality. They won't be able to investigate serious or systemic corruption risks because they may not fall under the definition of criminal conduct. They're saying they're producing an anti-corruption body, but in fact it's going to operate in such a way that public officials and particularly parliamentarians are actually going to be shielded from transparency. They're going to be shielded from accountability. An effective integrity commission must be public-facing. It should be able to act on tips and information from the public media and public officials, including whistleblowers. And there's no public reporting. And public hearings ensure that proceedings are not secret and it increases public trust as well. And also the post-integrity commissions can't receive complaints directly from the public. There is no avenue for a complaint by a public service whistleblower. There is no avenue complaint by a member of the public. There is no obligation on parliamentarians to report corruption into the body. There's no power for the commission to start its own investigations if it gets wind of a potential issue. And there's forced secrecy on the body. The current strict reporting lines of this model behind closed doors can actually breed mistrust. Please tell us what you graded Labour's policies for a federal ICAC and why. I gave Labour a grade of A. Well, Labour would only get a C, which is like a bare pass. I graded Labour's proposal on a federal ICAC, a B. I've given Labour a B. I would give it a pass mark, but a very, very low pass mark. What we've seen with the coalition policy is the promise, but then a lot of delays and it never came to fruition. Proposed anti-corruption commission by Labour is a promise that will happen within six months if Labour came into government. So there is a proposed timeline. The proposed anti-corruption commission can act in response to individual referrals, including whistleblowers and public complainants. The principles insofar as they go, they include things like the facility for public hearings, a broad definition of corruption, some of the fundamentals, that the coalition model suffers from badly. Labour's promised broader scope and powers, including discretion to commence inquiries into serious and systemic corruption on its own initiative. Labour's also promised a transparent commission with powers to hold public hearings and make findings of fact, including a finding of corrupt conduct. And that's important because we need a commission that is public-facing and that is transparent. So in summary, Labour proposes a robust anti-corruption commission with strong powers and coupled with checks and balances to ensure that it does not abuse those powers. I guess people want to see that any government or alternative government is putting its money where its mouth is. Both the coalition and the Labour platforms, they've been responding to a lead which has been taken by, initially by the Greens since 2010 and then more recently by independence of all parts of the political spectrum. It's only because the coalition actually then promised more for a weaker model that we ended up with Labour saying, oh, yes, well, we would match that for our stronger model. Well, you would hope that they would match that for a stronger model because a stronger model is likely to be more expensive. If you do it on aspirations alone, it looks pretty good. But you can't make judgments just on a set of statements saying basically, we'll do it better. Commission will be independent. It'll be able to hold public hearings. It'll have bipartisan support. It'll have procedural fairness and it'll be able to make findings of corrupt conduct and report those findings. The ALP appears to be on the path to a more robust anti-corruption commission than the government. But it's hard to know whether it's an A-ranked body we've got in our midst because we actually know relatively little about it. We don't have the same level of detail to compare when it comes to the Labour proposing. Questions, of course, remain over the design details because we just don't have that detail yet. We also wonder about the funding and the timing. These are the sorts of things that are still to be ironed out. If there are weaknesses in the detail or in the funding, a Labour government might need to strengthen their model to get the deal done. The Labour Party has put up a one-pager in contrast to the 347-page the government has put up. There's not enough information. A page isn't enough. But at the moment, we don't have a full draft of the proposal. We've got a list of design principles. They look promising. They appear to respond to most of the issues that have been raised with the government's model, particularly in relation to how narrowly corruption is defined, the ability to receive complaints from members of the public and whistleblowers, the ability for the commission to conduct its own inquiries and its own motion, the power to conduct public hearings in some circumstances. But these are all very technical, detailed things. I want to see the actual draft provisions that set things out like jurisdiction, the investigative bar, reporting requirements and avenues, and public hearing thresholds. I can't give an A away to a model that I don't have the detail as yet.


Hey guys! So I figured I'd jump in here real quick just to kind of give you a heads up on how this is gonna go because my last shopping trip was a really long one. I ended up going to two stores in the end and it ended up being a extremely long video so I figured you know what why don't I just break this up into two parts and have one video dedicated to each store. So of course like all the other ones the first half is gonna be the actual shop with me and then the end I'm gonna have the haul where I show you what I picked up from there and then in the next video will be the other store that I went to and that haul as well.  So you know what without further ado let's head on to Barnes and Obles. Oh my goodness we have a ton of puzzles here. This is not good. I wouldn't get 150% off for January. I got here at the right time. We have this here. I love this artwork. This is really cute. A jigsaw puzzle with over 100 clues to spot. What brand is this? Is that the brand Lawrence King? I don't know. This is a really cute image. I like that. We got an e-boo set here 1,000 pieces. This is really pretty. I really did enjoy this brand when I first tried it. I haven't gotten another one since but I don't know. Might be when I pick up soon. What else do we have here that I can try to reach? Oh we have galesan here. That's a fun image. Lots of feathers. I love the boxes. We have another galesan as well. This is beautiful. Look at this bouquet van. I want to go visit there. That's cute. How much are these? Okay I'm guessing $16.99 which is not terrible and I do need to pick up like an actual galesan. Not the one like I tried last time. I'm the good puzzle co. So that's that's one to keep in mind. What is this in here? We have zodiac power. This is another galesan set. Looks like we have a nice selection of galesan puzzles throughout. There's so many here. I don't even know what to bring down. Check out this galesan. This is gorgeous. So 1000 pieces. I love the artwork on this one. Check this one out. This is Piccadilly Circus in England. That's a fun image. I love this artwork. This is great. I don't know. I haven't tried an actual galesan 1000 pieces. That's one to think about. And we got a ton more here. This one is from Greenbox. Is that what that is?  Oh look at this galesan one. That's fun. I really love all of them. We have a dog park here. That's a fun image. We have a bunch of butterflies. How many pieces is this? Oh that's 500. How about the stickers right there? Open your eyes. Oh look at this. This is making me hungry. I'm gonna need some lunch soon but oh Jesus. They're all throwing themselves at me. What is this? 350 pieces. I don't know what this is. Oh I see.  There's no, it doesn't look to be any actual image that you create here. But that's interesting. Looks like they have a couple of them in different color schemes. Look at this one. We have a 500 piece brand. Puzzle designed by Scott Church. Can't play our critters. That's cute. But what's the brand here? Is that the brand? All port editions? I don't know. This is interesting. Does it keep image? All right. What else do we have? We have murder mystery party. This is, is that the brand? I guess it is. I'm not really sure. That might be the brand but we got a lot going on here. Has mysteries with a challenging twist. Interesting. This 1000 pieces. Oh look at that. Animal tails. Basically it's a bunch of book covers. Is that the brand? Remarks? Is that right? I don't know. That's fun. Got a bunch of book covers. Fa la la la. I don't know what that is. Oh it's just an image of gift shopping. We got this one here of just some stumps. This one looks like it's also from Remarks.  I like succulent plants. I have a collection of them at home because they're very easy to maintain. That's another Remark puzzle. Then we got ourselves some crystal 3D puzzles here. I haven't tried these before. At some point I plan to but they also have like a little castle here and we have a horsey and some more down here as well. Frogs. I love frogs. Look at him. He's got a little crown. How cute. And they have here some accessories as well. We have a stand and go. It's like a puzzle easel from Ravensburger. That's nice. Something like that at home. Oh I'm looking here. We have a puzzle mat for up to 3,000 pieces. That's massive. That'll be handy. Check out this hierographics. I love the packaging. It's like a little tin van. That's fun. And look at this. I love this. The packaging is amazing. It's like a book. Isn't that cute? What brand? This is Jigsaw Library. I love this. We have the great gas fee here. How much are these? Oh my god. I love this packaging. They're small puzzles. They're only 252 pieces but I'm pretty... Oh here are the others. We have Pride and Prejudice. We have Frankenstein. Oh wow. Check these out. We have bigger versions here. Murder most puzzling. Complete the Jigsaw to reveal the clues and solve the case. This is cool. Now these are interesting because it says the full puzzle image is a secret until you complete the Jigsaw. So you have really no idea what you're piecing together here. All you have is this part of the image. 1895. They're pretty up there considering it's how many pieces? 500? But I don't know. Oh my god. I love how they look on books. That's so awesome. It looks like this is a different brand though. I'm seeing Chronicle books. I could be wrong. Oh yeah. I think it is called Chronicle books but this is cool. We have the Missing Will and the other one there. I love these. These are so cool. Oh look we have a one of the blank puzzles here. That's a nice image. Look at that. That's a perfect place to be when it's literally cold outside. What's this? Lift each other higher. It's a matchbox puzzle. Look at that. It looks just like a matchbox. That's I guess that's why they call it that. Hello. This is a galesan. That's fun. I'm telling you guys there's so many here that I don't even know if I'm gonna get through all of these. We have another remarks puzzle here of horror book covers or horror movie covers. We have quite a number of these remark puzzles. Look at these movie posters. That's cool. This is like a panorama panoramic image. 1,000 pieces. Check out these. This is from Peacework Puzzles. Raz and Shannon. Got some what do we have here? Donuts, bagels. No it's not donuts. It's bagels. That looks good. We have fruit here. How much are these actually? 30? Wow. These are expensive. I wonder why? We're gonna have to find out one day, aren't we? Some more of these remarks puzzles. Different artwork styles. Look at all these random cats doing some weird things. Oh my god. Look at this. That is fun. We got a bunch of animals dressed up having a picnic. My god. I'm so overwhelmed right now. There's no way I'm gonna get through all this but I'm gonna do my best. Got this 500 piece here. Puzzles learned by Toucan Art. What brand is this? This is from Allport Editions. What else? Oh my goodness, there's so much. This is so cool. Stitch by stitch from Gallison. Oh my goodness. Look at that shop. Look at the cat. This is beautiful. Oh my god.  Oh what's this? Double-sided puzzle. 500 pieces. This is more like a photograph. The gray mallet is that? No, no. This is a Gallison. Hello. There we go. Oh look. So you get two different puzzles, I'm assuming. We have these tubes down here from, I'm trying to see the brands for these workshop, I'm guessing. These are pretty expensive, 31.99 for these sets, two printed art inserts, 1,000 pieces. Interesting and we got a number of them here. We have one here with a bunch of random animals kind of looking petrified. This one here looks like a little bookstore or just a bookshelf. I don't know. That's pretty, actually. We got this big one here. Check this out. Just a bunch of, I don't know what this is. What is that? Colorful cactuses or something? I don't know. Oh this one is pretty. Look at that. Let's just like some plants and roses. Got that one again. Got some more plant life here and the rest are pretty much the same. Those are cool. I like the packaging. It's interesting but I must say that, oh 28.99. That's pricey. That one's 28.99. These are 31.99 for the 1,000 piece and these are the 500 piece. We have one here from Professor Puzzle. 500 piece. This is also double-sided cafe and dog park. That's interesting. So you pick which one you want to do and work accordingly. Look at that. That's fun. You get two puzzles in one set. That is absolutely beautiful. This is New York City, the cathedral. St. Patrick's Cathedral. This is 1,000 pieces. Oh Clementoni. This is a brand that I have not tried before and if I see an image here that I'm really interested in, I think I may grab it. But again, I have to feel the image. This one is of Egypt. Look at this galsen. This is beautiful. This is 1,000 pieces. Paris, France. Oh I love this one. How much is this? 16.99. That's not bad. We have a Robinsburger here. That's pretty. I think I've seen someone on Discord did this puzzle and it looked absolutely beautiful when it was completed. We have some mud puppy puzzles here. This is 500 search and find. Look at this. It's so cute. Oh my god. I love this image. Oh this is a lot of fun. 45 things to find. I think I have a search and find puzzle at home but I believe it's from Masterpieces. But this image, this is really cute. We have another galsen here. That is really pretty. Oh, fruit trucks. This is 500 pieces from Professor Puzzle. 14.99 for this one, for 500 pieces. It has a, what is this? 2nd chain 500-piece jigsaw puzzle, pop-up puzzle piece sorter and poster. What does that mean? Pop-up puzzle piece sorter? I don't know. I love this image. Look at that. I love food trucks. Look at those donuts. They look so happy. You know I'm gonna be here passing through all the food trucks eating something. Oh my god. I love this image. That's cute. We have some white mountain here. We have more galsen sets. This is a foil puzzle. Oh my god. I don't know how I'm gonna get through most of these. We have an ocean anatomy puzzle from Story Puzzle. Interesting. Got so many brands here that I've never heard before. We have galsen here with books and different shops. Another one. These are, look at the colors on this one. This is gorgeous. Oh wow. Look at this. The world of Shakespeare. This is 1000 pieces. This is fancy. What is this? Guess the, I'm thinking the brand is Lawrence Key. I don't know. But I must say the selection of puzzles of Barnes & Noble is, I mean the packaging. These are like top notch. Like the selection is incredible. Look, we have a Robbins burger here. We have some more mud puppy sets. Oh wow. Check out this 3000 piece SpongeBob puzzle. This is from Aquarius. We got so much going on there. I don't know. This looks like it'd be a nightmare to complete. Oh wow. Check out this gradient set here. That's interesting. What brand is this from? Poster puzzles? Look at that. That looks a little scary to me to be honest. A pomegranate. I know some of yous have mentioned pomegranate before. We have one here. This is nice. Beautiful image here of a house. Most likely my. And these run for 2095. This one is a 1000 piece set. That's actually really nice. I like that image. I wonder if they have more pomegranates here. I'll tell you what though. They have a ton of galesan sets and they're so beautiful. This selection is amazing. Look at this one. This one is a foil puzzle from galesan. Sparkling city. 1000 pieces. That's awesome. There's so many here. I don't know. I don't know what to do. We have the world of Dracula. I love that book by the way. And the world of Frankenstein. I love that one as well. What brand is this? These are Lawrence King again. And these are spectacular images. They got a lot going on here. Probably a bunch of different scenes from the book which is fun. Makes me want to look at the Dracula one too. Oh my god. That's cool. Look at that. That is awesome. Oh we have a King Arthur here as well. Look at that. These look like they'll be difficult. That's cool. And the world of Charles Dickens. What does this look like? Oh my goodness. These look hard. But really fun looking. How much are these? These are $21.99. That's pretty up there but I mean just by the packaging they look fantastic. I think I would pay that. Starting to get a little loud in here. So I'm going to do my best. Oh look. We actually have another one from that brand. We have the world of the Harlem Renaissance. That looks really cool. This one looks really fun. I love the colors on this. That is cool. And look at these teapots here. What brand is this? This is Galison. I got these. Galison sets are amazing. That is gorgeous. There's way too many. We got some more Euro graphic sets here. But I do have plenty of Neuschwanstein castle images. This is another double-sided puzzle here. We have one side with a glossy finish and one with a matte finish. This is cool. Look at this. We have one here that's country many puzzles create one giant map. It's a map of Europe. It has 37 fun shaped pieces. It's 850 pieces. Wow. What brand is this? Oh it's Remarks again. This this location has a ton of Remarks puzzles. Oh look. We have another one of these the world of images here. Oh wow. I love that. Look at that. That's cool. Oh look. I found another Eboo set. The Alchemist home. I feel like I saw this online and I almost bought it but I don't quite remember. There's just so much going on here. We got a round Robbins burger set here. 500 piece circle of colors.  I guess the brand is Sibley or Potter. I'm not sure. Potter puzzles. There we go. Interesting. Oh look we got the world of Jane Austin. Oh my god I love these. These puzzles are so much fun and they have a good selection of them. I would have to figure out if I get one of these world puzzles which one I get. We also have the center aisle here with a bunch of these tubes from Cavalini and Co. Is that what it is? These are Japanese wood block vintage puzzles. 1000 pieces. Actually these are not wood blocks. My bad. This is just I don't know what this is. It feels like cardboard to be honest. I don't know why they say wood blocks for it. 25 still. This is still 25 but it's a very nice selection of posters in the image here which is nice. We have this one of the map of USA with national parks. We got butterflies which flowers.  We have more of the national parks and the packaging is really nice. Check this out. These are $25. These are these are up there but I mean look at the packaging. We got some more dog ones. We got some fungus. We got kitty cats. Check these out. More of the national park posters and this is cool. This is a constellation. A celestial constellations. Is that the same thing? Yeah. I don't know. Celestial map. This looks like it'd be hard though. I'd probably lose my mind doing this one but this is these are beautiful. I lost my mind before it. What are you making fun of me? Oh look what I happened to find on the floor here. I have some of these images already but that means they do carry some Thomas Kincaid Seco puzzles from Disney which is good to know. We have this fun Robbins Burger set here of the three little bears. Oh man look at that. I'd love to be somewhere like that right now. Sitting down enjoying the view with my wine and cheese. Here's another galesan. That one looks like it'd be super challenging but that's beautiful.  We got that white American diner white marley set which I actually have. We have this Robbins Burger here. 500 pieces. Ah we have a puzzle here from the New York Puzzle Company. This one's called Field Trip. It's 500 pieces and I wonder oh yeah there's another one here. We have another image. 500 pieces as well. We have this one here Rainbow Readers. That was a little hard for me to say and I don't know why. We got that one as well. Oh that's fun. I like that one. Oh I really really do like that one because I just so happen to see the word hotdog there. You can tell I'm getting hungry. Chicken dinner. Yes I'm starving. I need to hurry up so that I can go eat. I think that's all the New York Puzzle Company images that they have. The rest here as I kind of repeat we do have this Buffalo Mandalorian set. More of the galesan sets that we already saw. What else? Oh look at the Disney ones. This is beautiful. Look at this Ariel set here. That's gorgeous. This is from their collector's edition. This is 1000 pieces. Oh my god look at this one guys. This would destroy me. Have any of you guys tried this puzzle before because this looks insane. Looks like something that I would probably lose a lot of hair over but it's Mickey Mouse. Maybe that'll make it better. I don't know probably not. We have a Pinocchio one here from their collector's edition. We have Alice in Wonderland. Snow White. Oh my gosh. The selection is unreal at this location. We have a Pixar. That is gorgeous. Snow White again. Oh my goodness. This store is dangerous. It's a good thing it's far away from where I live. We got Pocahontas. What else? This is cute. Abandoned Toy Store. Oh wow. I like that. Oh we got another Disney with a bunch of Disney movie posters. That's fun. We got Dumbo. And that one again. My god the selection of Disney sets is insane. And then we got more Robin's Burger sets here. Oh look we got Farrowson. There's another Farrowson. That's the poster one again. Oh we got Lady and the Tramp here. Look at that. I love that movie. And Alice again. Wow. What a selection. And they got more Robin's Burger sets here. Look we've got Winnie the Pooh. We got like Pixar posters in this one. This is not Disney but this is Clementoni Panorama. Look at that. That's beautiful. That's a point. I haven't really seen too many Clementoni yet. And I'm nearly at the end of the puzzle selection. But look at this one. This is another Robin's Burger here. 1500 piece set. And we have some other very beautiful Robin's Burger images.  Just you know running wild all together. Canadian collection from Robin's Burger. Oh wow. Look at this. From the treasures from the vault collection. Minnie Mouse and Mickey Mouse from Robin's Burger. Look at this one. It's like a campervan scene. I love this. This is cool. That's 1000 pieces. Oh I remember this image. Remember that's me having my tea. I don't know whose dog that is though because I don't have dogs but you know it's a beautiful image. Got some more Robin's Burger sets here. That's a beautiful 750 piece set. Look at that one. I think I've seen someone on Discord do this one as well. Look this is you know our puzzle table here. We're working on a Robin's Burger set. That's a lot of pets though. Could imagine what damage they can do to your work. But oh look at that one. That's beautiful. I could be hanging out there right now. It's gorgeous. Oh look at this gala. It looks like a book. This is so cool. I love packaging like this. I mean you know you do pay for the extra beautiful packaging but you know that's nice. Makes for a nice display on your puzzle shelves. You got that's the one we saw already. Oh what's this camping trip. Let's go camping. Flower. I can't read. Flow puzzles. All good things are wild and free. Look at that. You know that's me hanging out in the tent reading a book. I mean of course look at the coffee next to me. Hello. Yes I love this. What is this? Flow workman puzzles. Never heard of that brand but I am really feeling this image. This is fun. I love this. We got another one of these book style galesan sets. Look at that. You know one of these is my houses and you guys are probably my neighbors as well. This doesn't make sense for me to put too many houses in one spot. Got some more galesan sets here. You know I have to say I still haven't seen any more of the pomegranate or clementoni sets. There's a bunch of galesans which is not terrible but that's really what I came out here for. So I'm gonna have to really look and see the ones that I saw and figure out you know which images I like. Check out this Aquarius set here. This is 3,000 pieces. A magical mystery tour of 100 Beatles songs. I love the Beatles. I grew up listening to that kind of stuff. That's an interesting image though. That's a lot going on and it doesn't look like it'd be easy. That's for sure. We got another Robinsburger here of a camping trip. This is beautiful. We have a 2,000 piece Robinsburger here of a lot of random things happening but it looks fun though. What is this? Oh wow look at that. Welcome to Extraordinary. This is really giving me like universal studio vibes. I absolutely love this. It's a classic movie. Oh wow look at this Robinsburger. That's beautiful. Busy city streets. I love this. Where is this? Dining in Valencia. I love that. We have this 1,500 piece counts set. This is gorgeous as well. A lot of people having a good time here. This one is called Romance in Cinque Terre. And then there's this puzzle which I actually have because one of you guys sent it to me. So thank you. We have another one of these Robinsburger abandoned sets here. That's cool. That looks kind of creepy actually. I like it. We got Gooby Doo. We got Flintstones. We got these owls looking quite scarily at you. We got Bunch of Rocks. And we saw that one already and that's pretty much it. Now as I said I didn't really see enough of the pomegranate or clementoni sets but I'm gonna kind of skim through these again and kind of figure out what I'm gonna go home with because you know I gotta take advantage of this sale. So yeah let's move on.  And it's actually been quite a long time since I did a shop this big. I think it was actually over a year ago at this point but it was one of my first like shopping haul videos.  But I am so excited to show you what I got from there. Now the number one aim of this shopping trip was to pick up brands that I do not currently have and brands that a lot of you have mentioned to me. So overall the shopping trip at Barnes & Noble's was a completely different experience because we're talking about you know much more expensive puzzles. So I was really really glad that I was able to make it during their January puzzle month sale. Now even though this was kind of like a shopping spree day for me I did kind of have a set budget in mind. Nothing too wild and crazy. But you know what we're gonna get more into like the cost of everything in the budget later on in the video.   And unfortunately what they had there wasn't really calling out to me. There was literally I think only one puzzle image of from each brand. So you know there wasn't really much of a selection from those. So I didn't pick those up in the end because you know I kind of like need the image to really call out to me. But anyways I did pick up some other brands that are very very new to me. And the first one that we have here this one is fun. This one is from the brand Professor Puzzle. And it's called Food Trucks. It's 500 pieces and it's 14 by 19 inches when it's completed. Now what I found very interesting about this set was that the back does mention that not only does it have obviously you know your your jigsaw puzzle but it has a pop-up puzzle piece sorter. Which is interesting because I've never heard of puzzle brands offering this in their packaging. So I'd be curious to see what that looks like. They kind of have like a little image here showing you what it does look like. But aside from that I mean I mean look at this image you know why I picked this right. We obviously got ourselves a food truck festival here. And there's nothing I love more than food trucks. I don't know why. There's just something so exciting about them to me. And we got a ton of them here.  You even got a ramen truck. There's just too much goodness here. And what made this call out to me even more was the fact that they're even showcasing a puzzle piece here with me in it. Waiting to everyone.  I love this image. This is gonna be so much fun to put together. Because I'm not going on but either way I mean this is gonna be fantastic. And I honestly can't wait to see what this brand is like. Now at regular price this 500 piece professor puzzle set is $14.99. But with the sale that they were having at Barnes & Noble's with buy one get one 50% off. This particular set only cost me $7.49 in the end. Which to me is a fantastic deal for what looks like is going to be a really nice you know much better quality puzzle set. Now the next puzzle set that I have here is so beautiful and it's called all things are wild and free. It is 1000 pieces and it's about 26 by 19 inches when it's completed. Now this particular set has two brand names on it. We have Flow Puzzles and we have Workman Puzzles. Now I'm not sure which one would be considered the collection of the brand. I'm assuming Workman Puzzle refers to the actual quality and manufacturing of the pieces. And I guess Flow Puzzle is like the collection where the image is from. But this packaging is great. It's really nice and solid. My only thing with it is that the box didn't come taped. So I did of course you know open it up to make sure everything was in here. It does include a small little poster for reference image which is nice. But I mean other than that everything seemed to be okay. But you know aside from the nice packaging of course this image is absolutely gorgeous. I'm obviously on my solo camping trip here. I probably just finished dipping my feet into the little river on the side here and just figured I spend the rest of the afternoon just peacefully reading in my tent with a nice hot cup of coffee nearby. This image is great. I love all the colors. I love everything that's going on here. I kind of feel like this isn't going to be extremely challenging. So overall I think I'm really looking forward to completing this puzzle and seeing what this brand is like. Now at regular price this puzzle is $19.95. But with this sale this one only cost me $9.97 which again another fantastic deal for this set. I think this is going to be some really good stuff here and for the price you can't really go wrong. Now of course I was charged full price for the other two sets because they just so happen to be you know the more expensive of the sets that I bought there. But for the next one I'm really excited about it because it is based on one of my favorite favorite books. And this one is called The World of Dracula. It is 1,000 pieces and it's 19 by 27 inches when it's completed. Now in terms of the brand I'm I'm not quite sure it. We have Laurence King here so I'm guessing that's what this is. And as you saw during the shopping part of the video there was a number of these based on different novels. But as I said Dracula just so happens to be one of my most favorite novels. I like Frankenstein too but this puzzle image like really got me in there because Dracula's castle is always portrayed as being so dark and mysterious. And I love that kind of stuff. And what I love about this image is that obviously you have all the different characters throughout the image. And like it says on the side here as well it includes all the key scenes from the novel in incredible detail. I absolutely love this. Now do I picture myself in this image? Absolutely not because you know I don't really want to find myself in a situation like this. But I love the artwork. I love the colors. Of course you know the castle is amazing. I love this. I cannot wait to work on this puzzle. I've never worked on anything like this before. So this is going to be a lot of fun. Now as I said this was one of the more expensive sets. And this one was $21.99. Now $21.99 is more than I would typically spend on a puzzle set. But to be honest I think it's going to be worth it because then you not only is the packaging great but I just love the whole concept of this. And I'm really excited to see what the overall quality is like with the puzzle pieces. And if it's something that I really really enjoy I just might end up picking up the other ones that I really really wish I could have gotten as well. Because to be honest these make a great display in your collection. So yeah I'm super looking forward to this one. And for the last set that we picked up in Barnes & Noble it is called Autumn Excursion. This one is 1000 pieces and it's 19.25 x 26.58 inches when it's completed. And it is from the New York Puzzle Company. Now many of you have brought up this brand to me. And it's one that has been on my radar for quite a long time now. So I was really glad that Barnes & Nobles had a number of these sets in stock. And out of all of the puzzles that were there I mean this one immediately caught my attention. Because not only do we have a lot going on here and the colors are just looks so vibrant and exciting. I mean this image is like really cute.  I could see myself sitting at that table there eating some nice fried chicken. And then afterwards I can go across the street and pick up a hot dog. I'm not kidding you that was absolutely the main reason that like made me like say this is the one. And as I said the image itself is amazing. I love the scenery. The artwork is fantastic. The colors are great. There's just so much going on here. And it just seems like it's going to be a really fun image to put together. And again we have really good packaging here. It's completely sealed in plastic wrap. And this was $22. I paid full price for this one. So yeah I'm really hoping that the puzzle pieces themselves you know are worth the $22 price tag. So yeah those were the sets that I got at Barnes & Nobles. Now that this Barnes & Noble shopping trip is complete be sure to stay tuned for the next video which will be the final part of this very long shopping day. But before you leave make sure to let me know down below if you've tried any of these brands and what were your experiences like. And also let me know which brands are you looking forward to seeing me try sooner rather than later. I really do need to start planning out what I'm going to do after I complete this 2000 count set. Which to be honest is driving me crazy so I'm really looking forward to hearing your thoughts. But if you're watching this after I post the next video I'm going to leave a link to it right over here so that you could jump right into it. And I'll also leave a link down in the description box below. But make sure if you are new here that you subscribe so that you could tag along with me on other shopping trips and hear what I have to say about those brands. Well guys I really need to get on with this 2000 count set. So I hope you are all doing well. Thank you all for watching and I'll see you in the next one.


First of all, thank you all for being here. I especially want to thank Councilman Brennan and Councilman Newt for being here as well. So this is a great day to dedicate this truck to the services of the fire service. This truck's run over 1300 calls a year, so we're very excited about being here today. And one might ask, why do we need a push in? The push in is a tradition that started back in the 1800s when there was a horse drawn fire apparatus. The horses couldn't write the trucks in. So the firefighters after every call, they were actually unhooking the apparatus. And they were pushing in themselves, so we were very excited about that. So I'm just glad to have both City and County here representing here today. Because they showed the collaboration and just their dedication to the fire service that would happen and so this time I'm turning it over to the two of them. I want to thank the Columbia Richland Fire Department. What you do for us, when I say us, I say every resident of the City of Columbia and Richland County. You have a large area to serve. Richland County is a big, big county. And funding comes from the City of Columbia and it comes from Richland County. So it's so important to work with my colleagues on City Council. And my friends and colleagues on County Council to make sure the Chief gets what he needs when it comes to manpower, when it comes to equipment, and when it comes to facilities. So Chief, I want to thank you for everything you do, your wonderful professional staff. And I look forward to working with Councilman Newton on the upcoming Columbia Richland Fire Department negotiations. Would love to thank you, to thank the entire fire department. And also to thank this engine. There was a time not long ago when I looked out my kitchen window and I saw bright lights and more bright lights. My neighbor's house was on fire and this is the engine that responded. It responded quickly.  And that's exactly the kind of service that we provide to all of the residents of Richland County. So we're excited to have this new truck. We're excited to support the fire services in this engine and we appreciate everything that our firefighters do for the community. Hey there, Mayor Steve Benjamin here. Thanks for watching this video. Make sure you give it a like right below the video and don't forget to subscribe. Also, while you're here, be sure to check out one of our other videos or follow on our social media platforms. Thanks again and remember, we are Columbia.


Boom headshot. Let's go. Hey guys real estate gaming here today.  It only cost a hundred bucks It's not too much. Okay, so let's see how our first game goes. Oh, no No tweeters. I don't think tweeters on this game with us. I don't think we can have any pads So tweeter won't be with us this game. Oh, no, okay preparing food fills you up food is yum food is yum I love food, especially pizza Running pizza. Okay. Oh Oh, cool. So it's actually like fortnight. You're in the little loading lobby Okay, what are the controls? Press Q to build X Okay, so this might Okay, where's all It's my take some adjusting for me, but I'll adjust it pretty quick Wait, there's only 20 people 21 Okay, like the bus is here. Wait, can we get on it? No, we can't. Oh, this is all we can Look this guy has a samurai sword Yeah, let's beat him up Okay, the 25 we have 30 seconds left. What can you dance here? Oh, you can't. Well, hi Okay I'm enough they have like tilted towers and all that or case.  Happy hillside sad settlement mini mountain Wonky well, oh, it's walking with us tightly town instead of the tomato town Lonely land instead of lonely lunch Okay, so how do you jump out? Let's go to tilt the towers. We're still the towers. Here it is We're topsy-towers. I mean not tilted.  You can only chat with your team. Yeah, well, I don't have a team Okay, so we're jumping out of the bus This is exactly like fortnight. This is pretty cool. They props to whoever made this game at and It's still an alpha. I believe Okay, so let's land somewhere. Let's land. Let's try to land at the top of the building right there. Oh, there's like three chests right there No, I'm not gonna make it up there. Am I? No, I'm not. Okay, uh, I Have bad luck We come oh, so we actually break the walls like in fortnight, too And we get where I'm mature. We have 28 materials Okay Where's the guns at? I'm just finding ammo. Are you kidding me? What was that a medkit? Okay, uh, it's not gonna do me very good if I don't have a weapon. Oh Nice we found the SNG Oh, no get away. It's my first time Okay So that guy's definitely down there Let's try to heal ourselves real quick. Okay. Nice. Let's go fight him now There's a chest right there. Oh, he's right there. Yes. We got our first kill. Good job guys Wait, he was shooting at someone, right? I can already have that assault weapon. Oh, I see a potion What is the green AR? Nice Okay, we have to be careful here, man Let's fix up our weapons in order Like how do you get rid of something? Drop Wait, I thought I tracked my potion Because I tricked the potion real quick man before anybody people before any people show up I had seen oh nice Oh no six Let's see what we get in this chest Better be something cool This is for tweeter. Oh, it's nice another shield potion Oh, it's a blue ak sweet So looks like we're gonna get rid of it Oh, this green one Okay, let's go back up there. Oh, there's more stuff Sweet Jesus Okay, so we have a little bit of tools. I keep hearing someone destroy stuff around me. That's not cool bro.  Nice I need a shotgun A silence SMG. Oh shotgun a pump Yeah, boy, we got a pump We gotta want this pistol. I thought I switched Let's get rid of the pistol Okay Now let's just get all the stuff in here and scram Let's go kill some other people Oh heavy ammo. I saw a chest. I can write yes Okay, so it seems like we're doing okay so far not too bad actually We're finding some pretty good stuff On this fort night.  We got the rpg man Isn't that sick?  Because then they're gonna try to surprise attack us But don't worry. I got a big surprise for them. Where are these guys at man? The guy already went throughout the whole map. Oh no, the smoke is coming Oh god, let's get out of there. We don't want to go into the smoke Oh, Jesus. Yes another chest. What should we get in here? tactical rifle What a rocket launcher Silence SMG. Oh attack shotgun Oh, maybe I shouldn't have done double shotgun. Wait, what? I thought I had my rpg. You know, why do I have band-aids? I've been running around with band-aids this whole time Where are these people at? I'm like roaming around the whole map The whole town and then I don't see anyone Okay, so it says there's 11 people left I don't see anybody though Oh, I see a supply drop all the way over there Okay, where can these people be at you guys? Hmm I see a car. I don't think you can drive cars here It would be kind of cool if you can though Oh god, where is everybody? It's so lonely out here, man. I should have put like squads or something, huh? Okay, somebody landed here And they'll like Oh, I hear the gunshot Oh, I see him I see the sniper though Oh, let's go Who is he shooting at though? He was aiming somewhere over here, right? I think that guy had a sniper. Let's go check out his stuff Oh, so I have the bird. Oh, he has a purple rocket launcher. Oh We came up on this guy, man Sweet Okay, let's go rifle Nice. Thank you for this awesome stuff Sweet. Now we have a purple AR A green shotgun A purple sniper and a purple RPG Let's go Let's pop our sniper out Is there somebody up there? I thought I heard something I hear like footsteps or something, man. Oh, I see a guy I'm trying to get a headshot Let's go Who is he shooting at? He was aiming somewhere down here, right? Oh You're messing with the wrong person, buddy What? Why are you running, bro? Why are you running, bro?  Come on. You can't do me dirty like that He's scared of me That's right. You better run away from me. Is he still up there? Oh god Okay, I don't know if I heard footsteps or it's just me 98 Okay, he's definitely hiding in that house The storm is closing in. Oh, that would be cool if you can ride that, man I would just get on that thing and go after that guy Okay, so let's try to get first place you guys We're trying to get that first w The first win of the game playing fortnite for the first time island royale. Okay, uh There's only five of us left. I don't see anybody else Okay, we need some help. Let's just use our med kit I'm gonna heal myself all the way up because it's always best to have a hundred health Oh I heard something I thought I heard some oh Some gunshots All right. Yep. Oh headshot. Let's go. Who saw that sweet headshot, man I just took that guy down like nothing Okay, so there's three people left Oh, man, why can't we get right that little golf golf cart, man? That would be so epic I would totally rush these guys Okay, uh, let's check if our guns are reloaded before we go in there and rush this boy To be careful, man. Check our backs Oh god Oh, he's over there Stop moving Where'd it go? He's somewhere over on that side Because so there's only three of us Oh, he got sniped Where is he? Oh, he's shooting at me How do you build? Not where he's at He's shooting. Oh, he's all the way back there. Come on reload faster. You sniper It's over buddy. You're in the water. Oh my god this drop It's like right here What second place?  Oh I'm sorry. We let you guys down We got second place you guys. Oh, it's all the way. We're so close. Remember this game isn't testing. I think it's finding much more Yeah, yeah, whatever man. So we just leveled up to level two and one match. That's not bad Is it right you guys? We thank you guys for watching. Thank you for the support and I'll see you guys next time


The forum may not be a new robot. Steamboat Willie. Walt Disney's first synchronized sound cartoon was the cartoon that raced the bar and made sound cartoons the new norm and officially introduced the world to Mickey Mouse. During the production of Steamboat Willie, there were a good amount of test animations made with accompanying dummy tracks to eliminate any errors in synchronizing since the recording would use a click track. As it turns out, Walt Disney Studios still has the original test reel deep within the vault. From rumors around the studio, the reel is labeled, bounce, sound film test, and the tests have been presumed to have been made in early 1928. The reel allegedly runs for 4 minutes and 15 seconds. Depending on who you ask, the contents of the reel can vary, but most sources can agree that half or even more of the test reel is short clips of sequences that would go on to be in Steamboat Willie, such as the sequence where Mickey swings a cat around or playing a cow's teeth like a xylophone. Other tellings of the rumor include instances of never-before-seen imagery mixed in with the normal clips. A few sources talk about a 10-second close-up of Mickey's face as he laughs, accompanied with the voice of Walt Disney doing his Mickey voice, synced to the movements of the chortling mouse. The laughing goes on for around 15 seconds before the screen blanks out. Some people refer to the expression on Mickey's face in this clip as slightly sinister in nature. On top of this, rare claims of instances of unsettling content have been made, including a 22nd clip of Mickey walking down an empty street, past five or six buildings on loop, with the only accompanying sound being random dissonant piano keys being banged on. The buildings look rundown and abandoned, the asphalt street and concrete sidewalk cracked in countless places, resembling spider webs. Garbage is carelessly strewn about, and a few rusty old-style cars litter the street, in a state of severe disrepair, pieces missing or dangling from the vehicles, becoming ghostly caricatures of what some have reported to be, screaming faces. Mickey's walking down is seemingly endless post-apocalyptic setting, as he looks down in a depressed expression. For the whole 20 seconds, nothing happens, except for walking. No evidence has come to light of this actually existing, but it's also rumored that during World War II, the U.S. Department of War commissioned Walt Disney to produce an animation for use in interrogating Nazi prisoners held at PO Box 1142, in order to extract information from them by psychologically torturing ones, who resisted threats of being handed over to the Soviets. What Disney allegedly presented them was an extended, 9-minute long version of the above animation test, in the exact same style as Mickey's original design. Mickey walks through the apocalyptic ruin of a city for a couple of more minutes, all while the jumbled piano music still playing in the background, before the distant sound of a man sobbing, loudly in pain, can be heard mixed in with the piano. After a couple more minutes, the sound of an old radio dialing through stations too fast appears in the audio. Mickey's walking begins to pick up a pace, like he's in a hurry to get somewhere, while the sounds of the crying man and radio static begin to crescendo, growing louder and louder, until all sound abruptly stops, and the film cuts to black. It remains black for a few seconds, just enough time for the viewer to think it's over, before the video and audio jump cuts back in. The audio is at its loudest point, with the piano sounding as if someone's repeatedly laying their entire arms across as many keys as possible, layered with the sound of a woman screaming for her life. The animation rapidly strobes between the cartoon and darkness, as a tight shot of Mickey's face shows his eyes melting off and drifting down to the bottom of his chin, as he smiles a crooked, tight lick smirk that slides upwards to one side of his liquefying face, his snout drooping downwards, his eyes now merged into a one formless block, dangling from what's left of his face. This all happens over the course of 30 seconds, before the camera cuts back to the standard shot of Mickey walking quickly down the decaying street, his face still having been melted. The animation starts to warble and contort, as if being viewed in a kaleidoscope, as the screaming and piano banging continues in the background, now with the sound of an old music box faintly being played. After a couple more minutes of this display, the image and sound jump cuts to the end card for all of the older Mickey shorts, with the usual happy-go-lucky music playing as the twisted cartoon draws to a close. Whether this was ever used in P.O. Box 1142 is up for debate amongst believers of this rumor. If this were to exist and have been used of course, none of those involved would admit this existed, or that any of the prisoners were submitted to anything dramatic, and all records of what happened at the intelligence facility have been destroyed following the end of the war. It is also debated whether the film real made for the war department was kept, or if it was destroyed as well. Some believers will tell you that the short was uploaded to the internet by an anonymous Disney employee, whose fate is also unknown. They also say that there's a chance you can find the morbid cartoon on the web, if you did enough. The title may vary, but they say it's most often found under simply, mouse, as the title. But of course, these are all just rumors. The topic is still discussed.


Hello and how are you all doing today? My name is Priyanka and I shall be helping you with the following question. It says, find limit x approaches to 1 fx where fx is equal to x square minus 1 when x value of x is less than equal to 1 and minus x square minus 1 where the value of x is greater than 1. Now proceeding on with the solution we must remember that limit of a function exists if the left hand limit is equal to the right hand limit. Why the knowledge of this concept is the key idea towards this question. Now here in this question we will be finding out the left hand limit. Now here in this question we will be finding out the left hand limit and the right hand limit. Now here we have the left hand limit of the function x is equal to 1. We have as equal to limit x tends to 1 from the left hand side fx that is limit x approaches to 1 from the left hand side. Now here the fx will be taken as x square minus 1 because when x is less than equal to 1 then we need to have the function x square minus 1. Further putting x is equal to 1 minus h we have as h x approaches to 1 therefore h will also approach to 0. So now we have limit h approaches 0 1 minus x square that is x square minus 1 that can be written as limit h approaches to 0. Now 1 a minus b the whole square is a square minus b square minus 2ab and we have minus 1 that is further equal to limit h approaches to 0. h square minus 2h now on simply substituting the value of h as 0 we have 0 the whole square minus 0 into minus 2 into 0 that is 0. Now we will be finding out the right hand limit of the function at x is equal to 1. It will be limit x approaches to 1 from the right hand side fx that is limit x approaches to 1 from right hand side. Now here the function will be minus x square minus 1 putting x equal to 1 plus h and as x approaches 1 then h will approach to 0.  Now on simply putting the value of h as 0 we have minus 2 minus 0 the whole square minus 2 into 0 that is minus 2. Since limit x approaches to 1 from left hand side of the function is not equal to limit x approaches to 1 from the right hand side so we can see that therefore the limit does not exist at x equal to 1. Right so this is the answer to the solution hope you understood the concept well have a nice day.