Hello everyone, welcome back to the session of ARIMA. In the previous few sessions, we have discussed the AR process, the MA process and the ARMA process also. Now, in this session, we will extend this AR, MA and ARMA process into ARIMA model. This is the last part of ARIMA process, entire ARIMA process where the data will be non-stationary. That means, in the previous couple of models of ARIMA that we have discussed whether it is AR, MA or ARMA, we assume that data are stationary. So, the over a period of time data are stable, but if the data are non-stationary, I have already discussed that earlier, but we will concentrate on that part now. When the data are non-stationary, you cannot directly use AR or MA process or ARMA process. You need to first convert the non-stationary data into stationary and then you can start your ARIMA model. So, ARIMA model is only for non-stationary data. So the process, if you look at the screen here, we have completed the basic understanding of SCF and PACF function because these are the two important ingredients or components which is required for the entire ARIMA process. Because you need to read the graph, the correlogram and understand the order of AR and MA process. So that for that reason, we need SCF and PACF. We understood that, then we have completed the AR process, the MA process and ARMA process. Now, we will be concentrating on ARIMA. Remember, ARIMA is nothing but when the data are stationary, then only you can use ARIMA. So effectively, if the data are non-stationary, you convert the data, say time series data. If the time series data are non-stationary, you convert them into stationary. This is the differencing part or I part. This comes as integrated. This term is noted as integrated. I will discuss more detail about it. And then once the data are become stationary, how to do that, how to convert non-stationary into stationary that we will discuss. And then you check once the data become stationary, either you which as it is AR process or MA process or ARMA process. So effectively, there is no ARIMA, ARIMA is all put together ARIMA only if data are non-stationary. If the data are stationary, your model completes here only. If data are stationary, you just either use AR process or MA process or ARMA process. ARIMA will not come to the picture. If the data are non-stationary, then only the entire steps you have to do. That means, first convert the non-stationary data into stationary, then AR process as per the correlogram graph AR or MA or ARMA and you complete the ARIMA process. So let us go to the last part, last leg of entire ARIMA process that is called ARIMA, auto regressive integrated moving average process for non-stationary data. Now if you talk about non-stationary data, you can recall the initial session, different type of data pattern that we have discussed or different type of data understanding of time series data. There we have discussed detail about stationary and non-stationary data. Let us recap that for a while. So if the data are stationary, what happens? You can see that this data, there is a variation, but it falls inside a band line to some extent. The outlayer or too much of you know uncertainty is not involved here. So if you take any block of data, you can see the mean, variance, standard deviation, etcetera, correlation all are to some extent constant. Here if you think the mean is here for this data block, you go to say next 3 months or say next couple of period for further. If you can calculate the mean, look at the mean is almost same, almost same. Little variation will be there if the data are straight line, then there is no point of prediction right. So little variation could be there, but overall data are steady, so these type of data are called stationary data for which you can use AR or MA or ARMA right. You can use any one of them, but if the data are non-stationary, in that case what happens? The basic definition says that data are non-stable right. So here if you think for this block, for say couple of in the middle of the data, if you take a 3 months pure data, you can see the mean is here, but if you come here, you can think the mean is here, you can calculate that. So therefore, mean has been shifted, mean has been shifted right. So you can see the changes of mean. Next time you do not know where the data will go, it might come back here also. So it is unpredictable. So therefore, this type of data are called as a non-stationary data. To some extent uptrend or downtrend data or you know seasonal data are also falls under to some extent non-stationary pattern. But here we are assuming that the pure non-stationary whether data are to some extent random in nature, stochastic in nature and it is not steady, the mean is shifting from time to time. So therefore, this data we will be considering as a part of ARIMA discussion, ARIMA not ARMA or ARMA that we have done only for stationary purpose. Now let us think about that. So suppose this is a non-stationary data, you have to convert that into stationary data and then you use whatever the model that we have discussed so far in the previous sessions. Now the point here is that if the data are non-stationary, we are discussing the non-stationary data, right? If the data are non-stationary, how to convert non-stationary data into stationary? One part I told about that you can take the logarithm, you can use some scaling of the data, like scale change, you can do that. Many way you can do the like you know conversion from the non-stationary to stationary. Remember that we have done the decentralization process in seniority class. How to do decentralization of the data by dividing by the index? That also we understood. There are many way to manage the non-stationary data to convert the non-stationary data into stationary. Here, we will understand one of the interesting process called differencing of non-stationary data and that differencing process we will use to convert the stationary and we will use that stationary data in the ARIMA process. Let us see how does it work. Suppose, you have a time series data say, time series data say y, ytc in general, y1, y2, y3, y4, y5, y6, y7 like this, right? You have the data. Now, what you do?  This is called delta, right? Delta y or delta yt whatever you can define or sometimes people define as a yt star or delta yt whatever you want, right? So, this is the difference you need to use. This will reduce the variation of the data. You can see one example and that data, this particular differencing data, these data sets, these data sets you need to use for your further calculation of SCAP, SCAP, ARMA process, MA process, AR process, etcetera. These data you cannot use because these data are non-stationary. In case this is non-stationary, then you convert this into stationary by taking a differencing. This process are called to some extent integration process or differencing process. Therefore, we call it as a autoregressive, integrated or differencing MA process. So, this is nothing but the differencing of ARMA or I-part of ARMA. Let us see one example. Here you can see the data, suppose sample data I have kept, how this data? If you plot this data, it is up-trend data. But if you take a differencing of that 4 minus 5, it is coming out to minus 1, 6 minus 4, it is coming out to be 2, 7 minus 6, it is coming out to be 1, 9 minus 7, it is coming out to be 2, say 12 minus 3, 9, it is coming out to be 3. So, if you draw this graph, it will be like 5, 4, 6, 7, 9, 12, it is like this. But if you draw this graph, it could be like say minus 1, minus 1, 2, 1, 2, 3, like the data are like this. Look at this. So, this is quite steady data. So, this data has been scaled down, it has been converted into this differencing data. So, this data is to some extent you can see steady. Over a period of time, you take this is steady, but this data is up-trend data, right, up-trend data. So, you cannot take that data because it is non-stationary to use for AR or MA process. So, you need this data. You can take another example, say suppose you take a data say 2, 4, 7, 9, say 13, like this say. It is up-trend data or down-trend data, but if you take a differencing, 4 minus 2 will be 4 minus 2, will be 2, 7 minus 4 will be 3, say 9 minus 7 will be 2, 13 minus 9 will be 4. So, this if you draw this 2, 3, 2, 4, you can see data are steady. So, these data are converting into a steady data. So, this is called the differencing process. You have to do that to scale down data to convert non-stationary data, non-stationary data into a stationary data. In seasonality we have done, here we are not talking about seasonality, up-trend or down-trend or different zigzag data that we are converting through differencing process. So, in this case if you think that first order differencing is not sufficient till the data suppose, suppose your data are like this, data are like this and if you do the first order differencing, first round of differencing your data might be like this. Still it is up-trend data, right, curvy data. So, if you do one more round of differencing, look at one more round of differencing here you can do delta say you know say delta star y t, delta star y t say or delta 2 whatever. You do one more round of differencing this minus this, this value minus this value. In excel you can do this, right. So, you will get one round of data, one round another in excel sheet, you will get one other column. So, this is called one further round of differencing, second order differencing. This data might be steady. Now, suppose here we have done this is a first on main data y t data. So, this is a delta y t say and you found that this is also non-stationary. How to check the non-stationary whether you have converted the data into stationary or not? That we will do in the next slide through the Kepler test. The testing part we will do when to stop. How many differencing you should do so that you are you can confirm that data becomes stationary that part we will discuss later. But suppose you are seeing that your data are non-stationary then you do one more round of differencing. In that case your data might be to some extent steady. You can think about this look at the third graph look at the third graph to some extent it is steady, right it is steady. So, mean is not shifting much. So, therefore, some epsilon error will be there, but data has becomes and now it is a this this this differencing we have done say for this particular data sets. Third round differencing second round differencing we have done. So, now data becomes stationary take this data the scale down data into your ARMA process ARMA process I part is over Arima's enter discussion is over now suppose. That means, I part is over differencing is done now you go to AR, MA or ARMA that is it this is what the enter process of differencing and Arima. Let us see the next part that you have a time series data and you found that data are non-stationary by drawing the graph or understanding the different calculation process then you need to convert it into stationary. But the point here is that how many round of differencing you need to do one round of differencing, two round of differencing, three round of differencing you have to stop somewhere right. So, that you can start your ARMA process this I part has to be completed now. So, for that there is a you know checking criteria whether the data has converted into non-stationary to stationary or not and when to stop that that been evaluated through Dickey-Fleur test. Dickey-Fleur has evolved on methodology, mathematical structure through which you can test the data in Python and different software it is readily available, but here I will give you the technical aspects of the testing part how does it work. So, Dickey-Fleur test says that this Dickey-Fleur test will be used for data testing whether the data becomes stationary or not. So, non-stationary data if you have let me use the pen again if you have a non-stationary data how to convert that into stationary and when to stop this we are going to discuss now through Dickey-Fleur test. So, it is a unit root test sometimes they call it is a unit root test which is a mathematical structure to check the stationarity of the data. So, let us consider a stochastic process where such that you know for your data say time series data Yt, Y1, Y2, Y3, Y4, Y5, Y6 like that you have and you can develop a you know formula like this say this is your error part say for the timing we are not focusing suppose you have found a correlation like you know linear formula of that of data with past data past lag and you found a correlation among them say. So, linear regression whatever some relationship you found with your stochastic data process. Now, if you subtract that Yt minus 1 from Yt you will find this formula right just from both side you subtract Yt minus 1 Yt minus Yt.  So, this constant if it become 0 after some it out of iteration if this constant become 0 your data differencing will become constant look at that the error part are there to some extent it is become 0. So, data become steady. So, no movement will be there now data become steady. So, therefore, this difference will become 0 if this become 0 if this does not become 0 then your data are non stationary still you need to do one more round of differencing and carry forward the testing part or differencing process. So, for that reason they proposed one hypothesis simple hypothesis that the hypothesis is that assume that phi minus 1 is 0 as a null hypothesis and alternative hypothesis is that phi not equals to 0 alternative is phi not equals to 0 right. So, if phi minus 1 equals to 0 that means, phi equals to 1 say whatever we are assuming that phi phi minus 1 not equals to 0 if you consider phi minus 1 not equals to 0 effectively alternative hypothesis is active, but if phi minus 1 equals to 0 in that case your null hypothesis will be active it means that you stop there this become 0 means this term let me use the highlight point this term become 0 means this term become constant this term become constant. So, stop here you do not need to do further differencing further differencing you just stop here in first round or maybe after one round.  To illustrate it further let us come to a fresh slide and I will explain in detail. So, that you know a layman person can also understand if you go to regression if you go to regression suppose you have a data set say x and say y right you have the data and you can fit a regression line say y equals to alpha plus beta x right epsilon part we are not discussing suppose alpha plus beta x suppose you have fit a regression say and in that case what do you do in in ANOVA analysis for overall testing of regression and the individual variables also we are considering single variables say. So, we propose a null hypothesis right what is the null hypothesis beta equals to 0 and alternative is what beta not equals to 0 what does it mean in regression it means that if now if p greater than say 0.05 0.05 say 0.05 we say that null hypothesis is active and if p less than 0.05 we say that alternative is active. So, that means, if alternative is active that means beta not equals to 0. So, there is a relationship between y and x and you can fit your regression fit the regression fit the line right, but if p is quite high greater than 0.05 then null hypothesis will active and in that case beta equals to 0 beta 0 means what there is no relationship between y and x. So, you cannot fit a regression line x is not explaining y or y is not explained by y. So, this is the basic understanding of regression analysis through ANOVA test and the hypothesis concept we all know this one right. Now, come back to our time series data suppose you have a time series data same concept we will use here now. Now, suppose you have a time series data y y 1 y 2 y 3 y 4 y 5 y 6 dot dot dot say. So, now, if you take the differencing as I mentioned say y t minus y t minus 1 right. So, it is nothing, but y 2 minus y 1 y 3 minus y 2 y 4 minus y 3 y 5 minus y 4 like this this right these are your first order differencing now.  Now, what you do we all know the basic AR model AR model of order 1 let us consider let us consider the basic AR model right and then this is the basic formula of AR model we all know subtract y t minus 1 from both side that if you will attest we are understanding now. So, now, what you do y t minus I know the hat part is there, but overall your basic understanding I am trying to pass to you subtract y t minus 1 this part you can think about this y t minus 1 u it will be what alpha plus say beta minus 1 into y t minus 1 t minus 1 plus epsilon that we are not discussing right. So, now, what happened this is nothing, but what this is nothing, but your delta y t delta y t right. So, the differencing is expressed in through this formula now this is what I have subtracted y t minus 1 from both side. So, it will be look like this. Now, this beta minus 1 is nothing, but this phi minus 1 of this phi minus 1 of the stochastic process of decay flux test look at phi minus 1 same logic. Now, what we will do we will propose a hypothesis say null hypothesis say beta minus 1 equals to 0 and alternative we are proposing beta minus 1 not equals to 0. Now, you do the p test if p value check say 0.05 you can check if the test is significant what happens alternative is active right. If p less than 0.05 this null h 1 h alternative is active now alternative hypothesis is active that means, beta minus 1 not equals to 0. If beta minus 1 become not equals to 0 let me put a highlight point you will get to know if beta minus if beta minus 1 not equals to 0 what does it mean. If not equals to 0 it means that this is not constant there is a relationship between the previous data and the current data. So, effectively what happens effectively what happens the data earlier you have taken and you have done the first order of differencing say still not this delta y say and this is y say this is still not stationary because beta minus 1 not equals to 0 not equals to 0. So, h 1 is active. So, you do one more round of differencing unless until the data become stationary, but in case your test is insignificant and you found beta minus 1 equals to 0 that means, null is active null is active in case null is active not the alternative is active. Suppose null is active then beta minus 1 equals to 0 null hypothesis is active if beta minus 1 equals to 0 what happens this part become 0 right. So, your data become constant data become data become constant. So, the differencing become constant if the differencing become constant what does it mean the data to some extent become stationary because this become constant right almost this look at this constant now little bit of variation will be there we are not focusing on that, but beta minus 1 equals to 0. So, it means that this data differencing is fixed now it is now steady now look at the data differencing first order differencing this is a delta y t right this is a delta y t this become steady now. So, delta y t steady means data become stationary you do not need to do further differencing stop there and go to AR or MA or ARMA process because data has become stationary now, but until unless your beta minus 1 or this differencing process does not hold true for null hypothesis you need to continuously do the differencing process. Here I have mentioned here you can see if the alternative hypothesis of the first degree of differencing cannot be accepted we apply AR process because first differencing are not required in the beginning itself your data become stationary, but in case the alternative is accepted alternative is accepted means what h 1 is active now active now in that case what happens if h 1 is active what happens you need to do differencing process differencing of differencing you continue that differencing of the degree D first order differencing D could be 1 D could be initially if the data are stationary D will be 0 if data are non stationary then do first order of differencing then you do the second order differencing third order differencing you continue this unless data become stationary this is what the Dickie Fuller test and once it is done you finalize your D you stop the criteria from this exercise of hypothesis testing and complete the Dickie Fuller test or non stationary to stationary conversion. This part is nothing, but the non stationary to stationary conversion of data and the stopping criteria when to stop through Dickie Fuller test there are many more method but Dickie Fuller test is very popular I thought of explaining that. So, I believe it is clear now now here you can see couple of examples. Suppose if D is 1 only one round of differencing you are doing right in that case you can select this model look at here D equals to 1 generally in ARMA process in ARMA process we use 3 component PDQ P stands for AR model we have already discussed that AR model of order P Q stands for order of MA model we have already discussed that D stands for the differencing part the differencing right. So, if D is 1 then one round of differencing if D is 2 two round of differencing that means, first initial data were not stationary you need one round of differencing and then take that data to your ARMA process. Look at the illustration here suppose this model here we can say that D equals to 0. So, data are stationary data are stationary it is nothing, but ARMA 2 1 because D equals to 0 data are stationary data are initial data were stationary right. So, you your D is 0 you do not have to do differencing look at here 2 actual data lack we have taken and one error this is the new noise white noise new white noise of your model you do not have to think on that just think the main error the model combination this is the AR part this is the MA part right this is the MA part MA order 1 AR order 2 if you add that how to add when to select the ARMA process we have discussed when are confused or you are not able to read the correlogram in that case you can take that or you know only 2 lack of like PSCF graph is positively standing line and SCF has a single standing in that case you can take that. Now, look at this this is what ARMA 3 1 3 order of lack old lack you are taking say it would be T minus 3 sorry and here only one error you are taking same logic here you can think it is we are simple taking AR 1 model, but differencing D equals to 1 one round of differencing you have to do then you select AR model look at one round of differencing you have done and then simply you have done the AR model look at alpha plus this some constant will be there could be in your model, but this is the white noise part this is what AR model look at this case here also you have 2 order of differencing AR 2 1 0 what means that you are not doing any MA process just first round of differencing and then you are using your AR process. In case your model are like this in case your model are like this say 0 1 1 in that case you have to select say you know say gamma 1 epsilon 1 plus say error part not here you have to take the first round of differencing say you know say delta this data you have to take and then there delta y t data you have to take and then there are error part formula the MA process that I have talked about is using this data you have to calculate your error part and the corresponding forecast then only you can develop this model of MA process with differencing data just take the differencing and follow the MA process you will be able to get a forecast, but you have to take the differencing data because that data is stationary the previous data original data was non-stationary. So, this way you can illustrate any type of AR MA or AREMA model right this is what the overall AREMA process auto regressive integrated moving average process I believe it is clear to everybody. Now, let us understand the overall steps of AREMA we have discussed the AR process we have discussed the MA process we have discussed the AR process MA process together now we discussed the AREMA also right PDQ D is the differencing the number of differencing of data you have done to convert the non-stationary into stationary. So, all this we have discussed now right 1, 2, 3, 4 now let us summarize this through the couple of steps first what you have to do the entire conclusion of AREMA process that 3, 4 sessions that I have taken that summary I am sharing with you now. Suppose take first take the data visualize the data understand the pattern draw the graph think whether it is a stationary or not if the data are stationary you directly come this step if the data are stationary you plot your SCF graph and PSA graph and select P and Q your D will not come into the picture select P Q depending on the your data pattern and the plot and the kind of correlogram structure you can select P Q and you can complete your model you can run the model. But if the data are non-stationary if the data are non-stationary suppose data are non-stationary if not look at if not in that case what you do you first do the differencing which we have discussed in this session today you first do the differencing. So, this is your actual data and do the differencing part take this data now and start your SCF and PSAF and check the ARMA etcetera because here in that case you might have a D equals to 1 or D equals to 2 depending on the number of differencing steps that you have done. So, if the data are non-stationary first you do the differencing and check the D key flow test which we have discussed now and stop there unless until data become stationary continue the process of differencing once it is done your D will be finalized D will be finalized here now D will be finalized and then you select P and Q based on that data and go for AR or MA or ARMA process there is no ARMA only ARMA or ARMA effectively only the differencing part if the data are non-stationary the differencing process has to be done and D key flow test has to be used to check whether the data become stationary or not. This conversion process comes under I part differencing part, integrated part because it is a to some extent a part of mathematical integration therefore, they call it is integrated but effectively it is a AR autoregressive differencing MA process that is it. Now one more part remember if the data are seasonal if the data are seasonal in that case you cannot do the differencing this way here what you are doing you are doing y 1 y 2 y 3 y 4 and you are taking a differencing y 2 minus y 1 right y 3 minus y 2. So, this way you are doing the differencing right, but if the data are seasonal in that case you have to take year on year basis differencing. So, quarter to quarter suppose you have a quarter on quarter to quarter basis data right you have like this say quarter 5 quarter 6. So, you write quarter 5 here quarter 6 here quarter 7 here quarter 8 here like this way is any quarter 9. So, this way suppose what I am trying to say share with you is that you when you take the quarterly data seasonal data in that case do not subtract from q 2 to q 1 to check your D key fuller or say differencing process you subtract q 5 minus q 1 because that is your say first quarter say fill quarter this is your a fill quarter of next year this is your say June quarter this is your say January quarter last quarter this is your December quarter. So, you quarter to quarter differencing you have to do look at here if the data follow seasonality then use 12 points differencing scale down the data by taking differencing if not immediate 12 point means it is a monthly if it is a monthly, but if it is a quarterly then you can take 4 period. So, it is depending on say 12 or 4 depending on the quarter like you know period whether it is a monthly data or it is a quarter leader if it is a monthly data then you have to subtract January to January February to February do not subtract from February minus January because it is not a sequential data it is a seasonal data. So, otherwise your variation will not be checked effectively and seasonality conversion to decennialize data or to some extra stationary data will not be done effectively because seasonality involved there, but if it is a quarter leader then you subtract from quarter to quarter April to April previous year April. So, the in this case 4 differencing will be done and then you can take the data and you can carry forward your forecasting process I believe it is clear to everybody. So, this is what the overall summary first you check the data stationary or not if stationary go to directly SCF and PSF graph select P or D and complete the model AR or MA or ARMA if not that means data are non-stationary you do the differencing if the data are seasonal then do the differencing in seasonal manner either month to month differencing or quarter to quarter basis, but in general if the data are non-stationary and steady data like you know in sequential data are they are like you know time temperature or etcetera or say crude oil price you are checking device or say stock price in that case what you do just take the older data immediate pass data and lack lacks and take the differencing. So, far what we have discussed and check the decoupler test once the differencing are done non-stationary conversion are done decoupler testing are over and then you go to that data and start developing your SCF PSCF and you know select your D select D selection are done PD and complete your ARMA model and make the future prediction this is the overall process of ARMA right. Here if you would like to see the final summary you can see for AR model overall summary your you know we know that correlogram reading your SCF will have exponential decay, but PSCF will have a cutoff right PSCF will have a cutoff SCF will have a exponential decay this is for AR model. In MA model in MA model for MA case this will become for MA case this will become your SCF this will become your PSCF detail we have discussed because SCF is sufficient to select for MA process because you are considering only the error term right only error term. So, they are already independent you do not need to check the multicollinearity or you do not need to remove the partial effect direct data you can take and you can because you have already done the check the data and only error for term you are adding in your MA process. Now, if you are confused and you are not able to select the model suppose both are having some you know standing point in that case you can select ARMA PQ or both are having exponential decay you are confused to select then you can you can select ARMA 1 or ARMA 2 to maximum. This is what the total summary of AR, MA and ARMA right and there is no ARMA ARMA comes only in the beginning effectively ARMA should come in the beginning, but I have discussed in my entire module of ARMA the ARMA part the final part at the end we have started with AR process we have spent significant time on that because that is the major part of model actual lakhs you are taking actual data you are taking and actual regression doing you are doing, but it is auto regression that is it and then you go to MA process if you want to include the error terms with the mean data that we have discussed then we understood the ARMA process and then we are going to ARMA because if the data are non-stationary then only you need to convert non-stationary to stationary and then this data you get and then you check either of them that is it. So, this is what the overall process of ARMA. So, now let us illustrate this ARMA model through one Excel data here we have come to the Excel and if you see this column, column number B here we have taken a new data not the TCS data. So, this data it is a recycling company US product handling company. So, cerebrine integrated technologies we have taken their data and this data to some extent follow the non-stationarity. The TCS data that we have illustrated earlier does not follow non-stationarity to some extent that was stationary. So, therefore, we have taken a new data a plus 3 months say like you know October to December same way and then this data we have plotted here you can see this data let me you know make it like this and then you know here you can see the graph look at this graph. So, this graph is nothing but a non-stationary data you can see here block wise it is changing. So, just we have taken 3 month data if you take more data you will get to know suppose this data is following non-stationarity here you can see that data is shifting from location to location. So, it is to some extent non-stationarity. So, you cannot directly run this data for your Arima model right. So, you need differencing. So, we have done the differencing here you can see the differencing this graph let us see first the process of differencing look at here we have done the differencing here look at y t minus y t minus 1. So, delta y t the way we have illustrated. So, if you make it increase the length of this you will get to know some yeah this all this calculation we have done here you can see suppose this one say you can see y t minus y t minus 1. So, this is what your delta y t. So, we have done this first order differencing and then this data this column number d will be your input data sets because this data is a stationary data here you can see the graph. So, suppose only first order differencing process we have illustrated here and the entire Arima calculation we have done like Arima process in the previous session we have done it, but you can use your Python and you can test all this DQ fuller process that I have told you. Now, suppose these data are stationary now first order differencing are stationary you can see the data now look at the data range it is 0.62 you know point minus 0.8 and it is in between the range it is the fluctuation has gone down too much right. So, it in between 1 gap 1.5 gap in the range. So, you can say that to some extent this data are stationary it is a it is a quite small range, but this one has a like 5.5 to almost 8.5. So, it is a big range where they are, but this data does not have much range. So, we are assuming that this data are say stationary. So, we have taken the first order differencing as our input data to the Arima. So, this is your stationary data suppose this column number d now what we will do let me put a color so that you can understand better you should not have any confusion. So, if you come here and if you put a different color say this color right. So, this is your differencing data first order differencing data we are assuming that this is stationary the first one are not stationary. Now after differencing you do simple Arima process that we have done you take the average of this data then calculate the center of them calculate the center of them right center of them and then next step you initialize your residual suppose it is 0 then you start your forecast. So, this is your beta and gamma you have to optimize it the way we have done in Arima process same we are repeating the Arima now just we have done the differencing right and then you get your forecast with your center data after differencing and then again you get the residual with your forecast and then again use this residual and the center data you get your next forecast look at here you get your next forecast and drag that you get the forecast. Now this is the forecast with your center data and the error term right. So, one term of 1 1 Arima 1 1 we have taken to some extent you can say finally Arima 1 1 1 you can see Arima 1 1 1 right because we are taking first order differencing d equals to 1 in this case d equals to 1 p equals to 1 q equals to 1. So, this we are taking right. So, now you get the forecast so this is your final forecast. Now you can optimize this here in this not in this sheet, but other in other sheet I have done the optimization also here you can see the optimization of beta 1 and gamma 1 you can go to data and you can go to solver and you can optimize the data. So, you have done the optimization you got the final beta 1 beta gamma 1 and the corresponding forecast come back to this sheet again. So, now here what you do you do the final forecast. So, final forecast here you I have written here you can see the final forecast look at the yellow cell let me increase the font size this final forecast are nothing, but in terms of delta yt because this is your center data this is your center data and this is your delta yt right. So, this forecast whatever you will get in terms of delta yt. So, here this is actually this forecast look at column number n this forecast it is nothing, but you are based on the center data like the Arma process. Now that if you go back that will be in your with in terms of delta yt. So, this delta yt minus mean data minus this mean data we have placed with small yt remember the small yt term of Arma model. So, that we have replaced now this is in terms of forecast of small yt. Now that you have to replace that you can read just this read just after calculation you will find this. Now this is your forecast in terms of delta yt not the final. Now what you have to do you have to replace delta yt with yt minus yt minus 1 that if you do here you will get any forecast of any period. Suppose here we have done the forecast for 25th period you can see here. So, now if you see forecast for 25th period are nothing, but the actual yt minus 1 of 24th period look at here yt minus 1. So, you replace this yt forecast equals to yt minus 1 will come here. So, yt minus 1 y24 b24 plus 0.002 the adjustment plus the coefficient beta 1 coefficient you can say into the corresponding delta yt minus 1 this is your delta yt minus 1 minus this error term here it comes as a minus, but in general it is another gamma right. So, gamma into the error term the previous error term you just do it. So, this is your forecast for 25th period with your Arma model in excel we have done the illustration. Similarly, I have shown one more illustration suppose forecast for the say 48th period. So, in order to do the forecast for 48th period you take the data of 47th period look at the data of 47th period the actual yt minus 1 and the delta yt and the error term because final formula we have done here. So, this in this final formula you put the data and you get the forecast this is your forecast you would like to see the accuracy level here you can see. Suppose for 47th I am talking about if you think the data here look at here. So, 48th period actually 6.8 and the error term if you see the error term is nothing, but just you know minus 0.21 and here if you see the forecast is coming up to be 7.1. So, it is almost closer to the actual forecast and the error term with your data sets also. So, therefore, this is the forecast for Arama model. So, what is the summary of this final illustration? First you do the differencing that means you convert the non-stationary data into stationary then select your order based on the differencing process. Suppose you have taken one order of differencing and we are assuming that this is the stationary data then you start your Arama process. So, this all this actually nothing, but the Arama calculation it is nothing, but the Arama calculation you can recall the Arama session. So, that we have done, but now you have to do the adjustment of your data. This adjustment because you have taken the difference we have done here and then you can make forecast of any period that you want you just follow the process and drag it you will get the forecast. This is what the Arama of final module or final process of autoregressive integrated moving average process. I hope it is clear to everybody. Thank you.


Hello Abby. Welcome to the show. Thank you for having me. Wonderful. Our good friend Joe Navarro had recommended that you would drop by and chat with us. He certainly has brought up your research and we were fascinated in going through your research for this show. There's a lot of ideas that align and we're certainly excited to hear some of the science behind some of the body language communication that we have been preaching on this show for the last 15 years. Hey I'm excited to get started. So we'd love to just kick it off and to get to know a bit about you. What was it about body language that got you interested? I think it was because human beings are so complicated and so individual that you can't say that anybody has a particular personality type or people do things for certain reasons. You know they're so difficult to understand. Yeah body language is a universal language. It's something that we've carried with us through evolution and we all share certain traits and characteristics and we all do similar things, similar reasons unconsciously in terms of our body language and I just feel that's incredible that we can identify these common patterns when everything about human beings seems to be completely different and I got really interested as everybody does when they start looking at nonverbal communication, lie detection and everybody wants to be a human lie detector and it took me some time in the field of studying lie detection to realize there is no such thing as a nonverbal cue of deception. I wrote two research papers trying to find cues for deception and we actually I mean the studies were really interesting because we took a really unique approach to the way we looked at body language but what we were actually just seeing is high stress and discomfort and then I changed my perspective when I was doing my PhD to look at cooperation and creating a positive environment so that people feel safe and feel comfortable and feel familiar with you that they want to share information with you and then it kind of opened up a whole world where everything seems really positive and you realize wow human beings are so cooperative and that is you know what we have evolved to do we've evolved to cooperate that is how we've survived and I think especially in academia I've always thought of everything is quite doggy dog and I know that business most apparently was saying your leadership is doggy dog but it really isn't because it is all about cooperation and trust and creating a positive environment for your colleagues and your employees and that's how you get to the top by working with other people cooperatively and that really is the key to successful relationships and successful business. Well we are certainly huge fans of cooperation and I know trust is something that a lot of us have this internal barometer around but what does trust define from a scientific perspective as? So this is an interesting question because scientists have this way of making things very confusing and they take these these concepts and then they pull them apart into okay well what's cognitive trust okay what's effective trust what's behavioral trust what's this kind of trust and they really pull them apart and make them individual but they overlap in so many different ways and I just think that it's over complicated and the way I see trust is safety you know if we feel safe if our brain says you are not a threat I trust you if I feel that I can be vulnerable and you won't exploit me that's trust. Now how quickly can trust be built if we look at it from that lens? So trust has evolved to be very very quick from non-verbal communication we actually judge trustworthiness in 33 milliseconds so it's literally the first judgment that we make about anybody before confidence before competence anything it's trust and it can be we can perceive someone as trust very very quickly but we can also perceive someone as untrustworthy just like that just as quick even if we've made that initial judgment of trustworthy all they have to do is one thing and our brain says no not safe and then it's gone so it depends on again the kind of trust that you're looking at if we're having an interaction now we have a one-time interaction then all your judgments are based on me in this one interaction but then if I am very very trustworthy and you think you know I trust you you seem trustworthy and then we have another interaction and I behave slightly differently all of that trust that's built up is gone so to answer your question it can be built very quickly it can be built over a long period of time and it can be destroyed very quickly and it can be destroyed after a long period of time if you've had this very very long lengthy trustworthy relationship one thing one simple thing and it can be broken down just like that with our clients one of the main points to building trust that we discuss is what after they come through they feel very good about being more vulnerable and being more open with new people because they learn its power so they want to communicate and build that trust with everybody and what they find after they have gotten comfortable with their vulnerability that other people aren't so comfortable with their vulnerability and what I tell them is that nature is going to play its course and everybody has a different rate of how and look for different things in order to get comfortable with people however the one thing that you can't do is you can't push nature you can't expedite it but you can remove the hurdles that are in the way for people developing trust and for a lot of people they think that it is an additive steps in order to build trust with people when in actuality it's removing a lot of the things that are getting in the way and keeping people from easily getting comfortable in building trust yeah and that's one thing that I think people get wrong that they think that trustworthiness is a tooltip you know we can talk about non-verbal behaviors to show the untrustworthy or behaviors to show the untrustworthy acts of you know the way that you speak and think and they think that they can apply these and use them and then form this trustworthiness and then put them down and they go off and continue with their lives and that's not what trust is because it's not a set of steps that you can just follow and then it's done it's something you really have to embed you can't just say okay well if I smile they perceive me as trustworthy and that's it and you know I'll apply these things at the beginning of the interaction and I don't need to worry about them later you're doing the behaviors at the beginning you stop doing them I'm going to stop seeing you with trustworthy just like if I like I said before we interact once I see you with trustworthy another time I don't it's not a tool kit it's a set of things that we understand can create a perception of trustworthiness but one other thing that creates trustworthiness is consistency we as human beings we need consistency it makes us comfortable it makes us so safe because it's predictable it's not uncertain and if we're interacting with someone and we don't know how they're going to be towards us are they going to be angry are they going to be happy are they going to be sad are they going to be there it creates uncertainty and it stops us feeling so safe in that interaction and if someone is inconsistent and they're using these behaviors as a tool kit they put them down sometimes pick them up sometimes put them down another time we don't feel safe we don't we can't predict how we're going to interact with them so you're exactly right and it is one of the most common mistakes that I think people make in the field of trustworthiness. Now you mentioned something earlier about as humans we are cooperative but there is this misconception that it's dog eat dog so can you talk a little bit about why trust and cooperation are important from an evolutionary perspective and why it is that we are predisposed to cooperation? Yeah so I think this dog eat dog perspective comes from the survival of the fittest you know I need to beat you so I can produce off-brain at this competition but survival of the fittest isn't about the traits that make you as an individual survive it's about the traits that make the group that you're in thrive and survive so those traits that enhance corporation and build trust those are the traits that flourish and those are the ones we've evolved to have and if we think that we've evolved in this really uncertain environment where there's threats everywhere you know there's a predator here there might not be my next meal here so having these group relationships has helped us to vital because you can rely on people they can hunt for us they can protect us all of these things that are just essential also reproduction which is quite self-explanatory that we need other people for those kinds of things and we need to be able to identify who we can cooperate with so the one way that we've done that is we've evolved these non-verbal communication tactics of showing trustworthiness so rather than just saying hey you know I'll cooperate with you we need to instantly be able to detect who was cooperative so we have evolved these behaviors which say I'm trustworthy we can pick out who to cooperate with and there's a lot of argument on this topic that well that can't be the case because people could use these tactics and pretend to be cooperative and just show these trustworthy behaviors and act to be a deceptive be deceptive but the thing is because we are a cooperative species that non-cooperative isn't going to last very long because in our social group we have profit so if someone isn't cooperative all it takes is one person to say they didn't cooperate and then the whole group know they're a non-cooperative so we don't need to look for you know tactics of these queues of deception that's not what we've evolved to look for we've evolved to be quick and look for trustworthiness and we see it in modern day now you know if you want to go to a restaurant what is the first thing that you do you look at google for reviews you look for what people said about it if you're getting into a new relationship and you know that they know a friend first thing you do what are they like tell me about them have they done anything wrong because we count on the gossip of other people and we see it in celebrity magazines and all of these things we we thrive on as a species because that when we get our information about you know who is effective and who is trustworthy and that's why it's so important not to view this as you said earlier as a toolkit because your reputation builds trust and if you're just turning it on and turning it off with certain people that you view as high value you know we use use this example in in class how you treat the janitor is exactly how you should treat the executive of the company because your reputation matters and that consistency is huge to building the trust that you're looking for yeah and you see incorporate a lot of the time and people say oh well you know it is dog eat dog because they're this way and they're up at the top they're doing amazing and they're not cooperative and they stand above people and it's like well that that doesn't mean that corporate corporation isn't the better way to go they might be successful with their manipulative tactic but it doesn't mean they wouldn't be more successful if they were cooperative people are successful all the time using negative tactics but just because people aren't doesn't mean that it's the only way to get there or the best way to get there just think if that person who is at the top for being manipulative decided to actually become trustworthy and be cooperative imagine how much better they could do and what you do see around people that have got that way and got to the top without being trustworthy and without being cooperative you see this bad reputation around them you see lawsuits and you see complaints and you see unhappy staff you see staff that don't enjoy their jobs and staff that don't enjoy their job what means you know a non-corporative work environment a non-productive work environment yeah I think especially if you've experienced that environment you don't thrive in a manipulative untrustworthy environment so although you may see that person leading you may also find that's not the culture that you want to be a part of or a company that you want to sustain working for yeah if you don't feel safe when you go to work and you feel like you can't see yourself around people you can't relax or that you know you have to do everything perfectly you know exactly how your boss wants it that puts you so on edge and it doesn't motivate you to do your best that motivates you to just get by keep your head down and get on with the job that's not what we want our employees to feel we want our employees to go to work and strive to be their best for themselves because they enjoy being there for their colleagues and because they respect their leader not because they fear their leader now with trust being built quickly I'd love to talk about these non-verbal cues that were evolutionally wired to look for around trustworthiness but yeah so it starts with a smile we know how important the smile is and the smile truly is a social signal think about when you go bowling when you hit a strike you stay completely straight safe when you hit the strike is only when you turn around and see people that you smile you communicate I'm excited I'm happy that's what the smile has evolved to do to communicate to communicate I'm not a threat I'm happy I'm happy to see you this funny thing happens when we see a smile and see a true genuine smile so when the upper cheek the raise and we see the Dutchman eyes it release it releases oxycosin and when oxycosin suppresses that fight-off-flight instinct where we say you know I might not be safe I need to go or I might need to go the smile relaxes us and just says you know it's safe it's fine and any behavior that could expose a vulnerability so we've evolved like I said in a really dangerous environment and one part of our body that we protect is our throat which is why when we see things that scare us or when we hear bad news a lot of the time we we put our hand to our throat without realizing we protect our throat or if something has you know we've had horrible news we often kind of stroke our throat and it's that instinct to protect and they could be you know a predator or something that could harm us so when we want to show that we're trustworthy we kind of lean our head to the side to do this head tilt and we expose our neck because we're exposing a vulnerable part of our body and saying you know I don't think you're a threat I'm not a threat he's a vulnerable part to show you that I'm not a threat and dogs actually do that too and I think this behavior was first mentioned in Charles Darwin's book on the emotions of man and animals and he noticed it from his dog and he saw certain behaviors in his dog and then it kind of you know we started to learn oh humans do these too and then we really started to figure out you know this is a signal to say I'm trustworthy at saying and also anything that is very open so things like open postures and open palms that I'm talking to you I have my palms facing outwards you can see what is in my hands I haven't got a weapon my hands are behind my back your brain says uh oh there could be something there in the hand so always making sure that you are facing someone and have your palms out and showing you know I'm not hiding anything from you and this is also why people that hide information or hold back information can be perceived as untrustworthy so when we tell kind of half truth and we hold a bit of information back and bosses do this all the time where you know there's some bad news but they're not really telling you everything it's that we don't know what it is that they have so our brain says it's it's the worst it could possibly be so we feel uncomfortable we feel unconsciously that they are untrustworthy because it's that same feeling of there could be a threat there I can't see that there isn't a threat so my brain says there is well what's so interesting in the work that we've done over the last 15 years is that we'll tell our clients hey smiling is important but internally they feel like they are smiling all the time yet they're not openly expressing that full face smile and it takes us actually filming them and showing them the video for themselves to show the discomfort that they're showing in these situations where they're feeling a little bit of social anxiety some tension and pressure and once they realize just the simple change in that smile and showing it early and often as you communicate with someone it leads to an entirely different interaction so we're also wired to respond in turn and mirror back that smile and bring energy to our communication when we feel the other person is bringing that smile in and showcasing us that trustworthiness so really changes the tenor of the entire conversation yeah it's emotional contagion so if someone is showing you I'm smiling I'm happy I'm really excited you kind of get just instant more energy from interacting with them because you take on some of their emotions just like we have all been in a conversation with an energy drain where you are excited and they are so just mellow and their total voice is mellow and their behavior is a mellow and then you just start to feel tired it's the same thing it's just that we mimic people unconsciously and through that we take on their emotions and we can't help it again that's an evolved behavior and that's why I did my phd in unconscious mimicry and it really does work through emotional contagion so I read this article a while ago and it said that people that show some anxious behaviors are perceived better and I don't know where they got their science from that if we interact with someone and we show that we're anxious that perceived is more trustworthy and makes people more comfortable and that really isn't the case because when we show that we're anxious they feel anxious they take on that anxiety so especially in the field of non-bubble communication there is so much rubbish out there and this is an example of some rubbish that's out there and you know we do have to be very careful about what we read because these kinds of things there's other ones about you know you can tell people's personality by how open or closed their posture is and things and when we take this misinformation it causes us to interact with people differently so if we perceive someone as hiding something because they're crossing their arms we're going to interact with them like they're hiding something or if we see someone as being defensive because they're showing certain behaviors that we misinterpret as defensive we're going to start making them defensive by the way we talk to them so we have to make sure that we're being careful of one how we interact with people because of emotional contagion because we're passing them our emotions but also because there is a lot of misinformation that we have to be careful how we are interpreting their behaviors and responding yeah I think it's far more important to focus on what you're communicating outward than to start like you did seeking out deception lie detection and reading all of this in the non-bubble communication sure that would be great if we could just look at someone and instantly get a 100 accurate read on them but what's far more impactful is actually modulating our own behaviors showcasing these trustworthy signals with everyone making it a part of our personality to build and grow trust with others knowing that it improves our reputation and improves our communication and of course through cooperation it gets us ahead in our career for a lot of people as well the idea is that they they come to us for and certainly for the men they want to learn to approach women and but also in a networking event to be able to walk up to somebody that they're interested in talking to and make their pitch and so and for the ladies as well as they want to be able to break the chains of their social anxiety and walk up to folks that they find interesting and chat with as well and due to that without them realizing it what they end up doing before they come through and learning about this is they go out of their way to make the other person feel that they can trust them that they're not up to something so what they'll do is they'll put their hands behind their back to show that I'm safe and they'll shrink themselves and all of those behaviors as you mentioned give off a different vibe to the person that they're talking with and they're now uncomfortable and so they leave and it's fascinating how easily we pick up on others body language which also brings me to this point that you mentioned about how we're going to mimic the micro expressions that are going on and we can and we see those when we're dealing with people but this is something that we're now learning that we have all this technology and I can't read the micro expressions on your face through zoom through the technology and so these interactions are almost they're very surface level yeah I'm talking with my mom and we have this opportunity to chat via cross the country but it's not like I'm sitting with her on the couch and and our the nature takes over and we're mimicking each other to understand and have an empathy that phase the face level yeah I mean I move away from micro expressions as it's not really an area that I place myself in and I look more at what we can observe and things that we can see and assess for but virtually what I have found is it doesn't actually affect how much you can create trust we can create trust and cooperation exactly the same virtually it's just people aren't used to it because our brains have not had to deal with it we are what our limb existence it's still you know hundreds of thousands of years ago reacted to that kind of environment we didn't have laptops back then so it's all very new and we don't really know how to respond so we actually really are natural way like how we are now based on that's not natural when you usually have a conversation with someone unless it's at a restaurant typically you're more to the side it's not actually if I stood the straight on with every conversation it is quite intimidating but yet we do that online and again that has picked up as a bit of a threat and we typically stay really rigid as well we don't move so much and that rigidness creates untrustworthyness we don't do the head tilt and again untrustworthy and what people tend to do online is they don't have much of the upper body showing they'll have their face really close to the camera or just kind of the camera way down looking up and we create trustworthiness and comfort through our body language to our face expression if you are in a really dark room or have a really bad camera or the camera is at a really weird angle I can't see your face expression clear enough to respond to them so it's not that we can't it's that we we don't realize how effective this tilt is virtually so we do it wrong and as well we actually have more of a power virtually because we have more control yeah we don't have the lower body anymore which takes away some power however when we're interacting in person we are in this moving environment where there's so much to control for and so much to think about if we are virtual I have complete control over this square that I'm sat in I have control over what's behind me I have control over what I'm wearing and how I act how much you can see and the light you know how close I am to natural light all of these things so it actually is almost easier to create trustworthiness and one thing that I always do is I have plants behind me because when we see greenery especially leafy plants it slows down the nervous system and creates calmness also light colors just a nice white background whereas a lot of people have really bad lighting or one thing that we see a lot that is really bad for trustworthiness is the filters that people put on their cameras yeah they have the the background I was in a meeting and someone had a lego house and everything they were saying I was trying to concentrate on what they were saying but I was just thinking you're in a lego house I can't stop looking at that area around them I kept staring at it and it takes our attention away from what they're saying and our limbic system has a lot of old to deal with this kind of stimuli so it's distracting and it's confusing for our brain to have this kind of interaction with these things in the background so we just need to be aware of the power we have virtually to create this cooperative and trustworthy atmosphere and really you know think about it for our meeting well I know with zoom and even in this interaction I've shrank my own screen many of us will get caught up in staring at ourselves and then become even more self-conscious instead of being direct with the camera removing the view of self obviously when we're interacting in person unless there's a mirror behind the person you're interacting with very rarely do you see yourself think about your own body language movements and how you're communicating but zoom has created that feedback loop which often robs our ability to listen actively to convey the trustworthiness that we're after now you did talk about the lower body being cut off I'd love to talk about what are those nonverbal signals that we're sending with our lower body that do help in building trustworthiness and so a really interesting study that I've recently done is looking at the power of the lower body to create perceptions of approachability so we talked about this orientation facing someone and orientating towards them and we know from research that when you orientate towards someone you're perceived as more approachable you're perceived as more warm and inviting and I wanted to see if okay well what about the lower body what is my upper body is facing towards you but my lower body is facing away and what about my foot specifically because we know that the lower body has an effect because studies have shown that the feet are on it so when we're nervous the rest of the body is saying I'm fine but the foot is tapping away because we think that people can't see it so if we're trying to control for our behaviors we think about my face my hands my upper body but we don't think okay I've got to control my feet we just kind of let them do that thing which is why I'm really interested to see if the feet carry any effect and what I found was that using a male and a female individually as targets so they had their upper body facing towards an observer lower body either facing towards or facing away and lower body facing towards they were perceived as approachable lower body facing away they were perceived as unapproachable statistically significant but what was interesting is the sex of the target didn't matter sex of the observer didn't matter what also didn't matter was how introverted or extroverted the observer was the only thing that mattered was the foot orientation and it just shows you tiny behaviors moving my foot towards or away from facing you can change how approachable and perceived and that's incredible and I did another study recently and it actually came out with this open versus closed gestures that I've been talking about but the finding was accidental because I wanted to see people's lower bodies when they were uncomfortable so when they were in an interview and the interviewee and the interviewer was you know a bit out of order so something too personal something a bit derogatory that makes the interviewee uncomfortable and what we saw was this sequence of people make themselves small with their lower body when they're uncomfortable they bring their knees together they tuck their feet below their chair but it's important the sequence that occurred so if I tuck my feet by my chair and they keep my knees out that doesn't actually indicate discomfort it's doing a number of these behaviors so bringing my knees and keeping my knees and then tucking my feet and then keeping my legs closed things like this where you see multiple closing gestures that's what indicates a discomfort and interestingly behaviors that we do associate with discomfort like we have blocking display so we kind of put our hands on top of our genitals and we feel attacked and we kind of protect ourselves and we a lot of the time we do cross our arms when we feel attacked but it isn't indicative of it and that that's the mistake but it is something that we do but it doesn't mean that when we do it that is what we feel and but we saw these blocking displays in all groups comfortable versus uncomfortable because of the context so it was the interview causing some discomfort display but the tucking of the feet and the bringing the legs together that was only to do with the interviewer making them uncomfortable so again it speaks to this importance of recognizing what displayed actually means if we said you know any time they show a blocking display they're uncomfortable and making them feel this way if we just went off of that because this one behavior means this one thing we would interpret it differently we would interpret it wrong because we don't take the context and it's the same virtually interviews create more discomfort so we're likely to see more discomfort display so because of virtual environment if somebody is showing anxious displays regularly despite you showing trustworthiness doesn't necessarily mean you're making them uncomfortable if everything else is saying uncomfortable i trust you but they are showing you know a couple of displays we see those behaviors in a virtual setting because it is unnatural we just have to take it in the bigger picture are all of their behaviors or most of their behaviors showing we discomfort or is it just one and then everything else is saying comfort because if it's just the one that's likely to be their pacifier that's likely to be the one thing that's there outlet you know i put on my pen sometimes or you know a lot of people touch their face or jiggle their foot and that's their pacifier has nothing to do with you has nothing to do with what you said it's all the other behaviors that you have to take into consideration as a whole and i think that's why it's so important for everyone to understand that again putting more emphasis on the signals that we send understanding that we actually have some power we can get people to mirror us we can add energy and trustworthiness to any interaction versus the opposite just observing and looking to read people based on these snapshots and tiny signals that we read online mean oh this person doesn't like us or this person is untrustworthy it just doesn't really add up effectively to reading communication it's better to start looking at yourself and projecting outward the confidence of trustworthiness that we need to build better relationships to build cooperation now this begs the question can we overcome distrust so can trust be rebuilt if we've made a mistake if we've showcased untrustworthiness or maybe we had a bad day and we didn't show up the same the previous way that we had shown up in interactions can we rebuild trust so we can rebuild trust but it depends on what broke the trust and it depends on how you go about rebuilding it and because people just say sorry and sometimes an apology is enough but an apology has to be appropriate for the condition so if say you embarrass me in public and we're really good friends close the trust you embarrass me in public and my trust is broken down and you want to apologize a simple apology isn't going to be enough it has to match what broke the trust so you're taking me into office privately and saying I'm really really sorry likely isn't going to be enough it has to match that embarrassment I felt I have to feel like you're doing something that makes you feel vulnerable or you feel embarrassed to match with how I felt otherwise that apology actually has the opposite effect so we just have to make sure that we take into consideration what broke the trust and the way we go about getting it has to equate to at least what broke the trust because if it doesn't and it's not enough it doesn't just not work it actually has negative consequences that it brings the trust even lower down so those really quick I'm sorry I didn't mean to I'm really sorry and we just throw them out thinking I know it's better than nothing it actually isn't better than nothing it's a lot worse than nothing because it reduces the trust even more so it sounds like in order to rebuild trust we have to understand how the trust was lost it's not something that we can flippantly rebuild and it needs to match at least the way our contrition needs to match the way the person felt in their losing trust for us yeah and we just need to remember sorry isn't better than nothing don't throw around those stories I won't do it again sorry because that can reduce the overall trust and it can reduce your perceived trustworthiness in general too so we have to make sure that you know that's saying don't tell me your sorry show me your sorry no it really is important that your behaviours say truly I am sorry and I'm going out of my way to do something that is negative for me to show you how sorry I am there has to be some kind of positive yourself because that's that's what an apology has really been designed to do to say this is negative for me this is something that I don't want to do I'm having a negative consequence for doing this so I'm doing it to show you how willing I am to gain your trust that if that story doesn't cost you anything then it isn't actually showing that you really want to rebuild that trust right so it doesn't value the relationship in a way that would rebuild the trust now what strikes me from all of this is the consistency that we need in our nonverbal communication and what we found with a lot of our clients is nonverbal communication is not something that many people even think about or are conscious of so we use video work in our classroom to really showcase and highlight some signals so they can start to clue themselves in and be a bit more conscious so in listening to this we heard a lot of nonverbal signals that are important for trustworthiness where do you think our audience should start if they want to start bringing these nonverbals into their communication in a more consistent manner so I think it all starts with education because like you said you know there's so much to learn that when we are focusing on ourselves and focusing on them trying to decode them and display it's too much that it becomes uncomfortable we do eventually have to realize that it is a system so we observe others and the step says and respond correctly and then show us so it is this cycle we have to understand it but unless we start by first okay understanding what do signals mean learn what signals show trustworthiness and really go into the site read the literature read the research and start you know figuring out how to improve yours start implementing it start seeing a change and then start trying to assess the others but it starts with education and it is a difficult process because learning anything is uncomfortable and we think our body language is easy but it is like learning a whole new language we have to figure out what things mean and it's complicated because different cultures have different things that mean different things so depending on you know what gender what culture what context and interact with people is going to change how our non-verbals are interpreted so we have to just start somewhere start with the basic start reading start getting educated on the display and then start implementing them well I love that linking it to verbal language because you don't get fluent just from reading a couple books and doing a couple workbooks you get fluent from actually implementing and practicing the language the tenses etc same thing with non-verbal communication you get fluent by bringing it into every interaction you're having not just picking and choosing on the job interview or the first date or when you're in the elevator and you're pitching someone but instead look at it as something that you can practice and hone in every interaction that you have and what I love about it is you do get that back because of the power of mirroring when you're adding these new non-verbal trustworthy signals people start reacting to you differently and it energizes you and it adds to the communication versus what many of us who aren't conscious of our non-verbal communication we're getting into boring small talk situations we're taking energy from the interaction and people aren't responding in kind and of course it feels like a lot more work than really just adding that smile now there is another piece to this that we hear a lot of misconceptions around and that's eye contact and I think many people start much like you around okay lie detection now I get all into eye contact am I making enough what's too much oh I heard if I look away that means I'm not trustworthy so I have to maintain eye contact so what are the right balances with eye contact and how can we use it to our advantage when it comes to trustworthiness and maybe what are those myths that we can dispel for audience around eye contact so in terms of the myth we think that people that look away are lying or people that look away are hiding something and that just isn't true people look away at the time they might be uncomfortable they might be very comfortable but they just don't give much eye contact in terms of how to give good eye we have this sort of optimum square and it's from the nose to the eyes square triangle sorry from the eyes to the nose and it's this this is the business gate the eyes to the nose and that's where we look and then we kind of have a more social gaze which is from the eyes to the mouth and then that's where we look sort of in a social setting and then we have the intimate gaze which is the eyes down to the chest so you wouldn't look from the eyes to the chest in a business setting like you should also avoid in a business setting looking from the eyes to the mouth you stay within that business game so that's kind of a good paradigm of where to look in different settings in terms of how much to look I don't think there is you know a perfect amount of eye contact to give also because people differ in how much eye contact they like to receive so give good eye contact you know regular eye contact but don't stare at somebody because that makes them uncomfortable and just recognize you know do they look like I'm making them uncomfortable by looking at them too much and if they they start to look a bit nervous let's just move your gaze away you don't have to completely turn and ignore them but just you know flip to other things and show them you're listening and then kind of flip to other things and show them you're listening again so just you have to figure out how they're comfortable and how you're comfortable as well because if you're thinking okay eye contact eye contact eye contact you're probably gonna miss the fact that they're like why are they giving me so much eye contact it's uncomfortable so don't think too much about it I would just stay within the correct gaze frame and then go with what feels comfortable and that is as much attention really that I give to eye contact because I think it really is again just that simple that we look for this perfect amount or perfect equation for things and we over complicate it and then struggle to do it perfectly and we've heard in the past that the direction that you're looking when you're breaking eye contact is accessing different brain cues is there any science around the direction that you're actually looking when you break eye contact no no I mean we do look in different directions when we access different parts of our brain but I mean we use a hundred percent of our brain you know most of the time there isn't a part of our brain that isn't active at some point um so I think that sits within that myth of you know we use 10 percent of our brain that's saying you know we um if we're creative we only use the right side or the left side all of these things same with you know we look in a certain direction when we're lying that you'll fit within that paradigm of just myth that you know again don't think too much into them because there really isn't any science backing them. Now with all of this research that you've done on nonverbal communication how have you brought it into your life is there anything that you've changed or now utilized from the research you've done in your nonverbal communication? Yes so I am not a touchy-feely person at all touching has always made me very uncomfortable but touching is something we have evolved to do it makes people feel very safe so because I know that that is um something that makes people feel safe same with you know open gestures I was always a very nervous person very very closed off I didn't really like being you know touched at all I did not like touching other people but I learned how powerful these are so I learned to get comfortable with them and it took me time because like you said it's not a toolkit you have to actually get comfortable so I I implemented what I know that that makes other people more comfortable because you know isn't that what we want when we interact with people we want to make them feel comfortable we want to make them feel good we want to make them leave the conversation thinking so nice to talk to that person I felt really good I felt safe so if you know that you do behaviors that aren't perceived well but they're comfortable to you try and learn to do the other behaviors learn to get comfortable with this stuff and make other people feel safe and you know anything is it's practice and it will become a habit eventually and now I'm a lot more touchy-feely I'm very open I have my hands out a lot and I'm always kind of armed out and things like that and you just you know eventually one day you think oh I don't even think about it anymore that's the best feeling in the world when it becomes who you are and how you act normally without having to be so conscious about it but it does take some conscious effort to get there and we all have these I mean that's the the beauty of nonverbal communication is we have conditioned ourselves to self soothe maybe it's looking at your phone maybe it's putting a drink in front of your chest maybe it's rubbing your stomach or grabbing your neck and yeah you may have to break a few bad habits but this is something that you can practice with everyone every interaction is an opportunity for you to practice your nonverbal communication and and now with the power of zoom we can do it in a more controlled environment like our home our office etc yeah and we can record ourselves and it's very uncomfortable I find uncomfortable seeing myself do anything if you watch a video or a talk of yourself it just it makes you crazy but you have to learn to kind of get comfortable with that do a talk and record yourself doing it or have an interaction with someone record it and then assess your behavior after and look at what did you do and how would they react to it or what did you do wrong what did you do well and learn to get comfortable with your own behaviors and assessing yourself well that's the best part about it because the cringe actually means it's impactful so we just had a group of military special operators through the program and they have great body language they've obviously taken great care of themselves to be in great shape but even watching themselves on video they were cringing they couldn't believe that they looked and appeared that way and the second round of video work instant change because they consciously seeing yourself feeling that cringe you want to make the change versus me saying hey you're not smiling enough Abby internally you're like AJ I'm definitely smiling but when you see yourself on video that you're not smiling it just carries much more weight with your subconscious mind to make that change yeah because you think when you see yourself you can put yourself in that other person's perspective and say you know I feel this way seeing myself my god that is how they must feel interacting with me and that's not how I want another person to feel I want them to feel good and comfortable and not cringe so I think when we watch it in cringe we just have to think okay do I want someone else to feel that way and what can I change so that they don't exactly such a valuable lesson well we love asking every guest what their x-factor is what personality trade skill set makes you so unique Abby um I think my ability just to keep going no matter how many times I fail at things I would just keep going the amount of failed studies um before I got my phd I had loads of rejections you just keep going failure really just means you know one less failure to go until I get what where I want to be I love that work in our audience find more about the work that you've done the research that you have so you can find my profile on my website which is abbeymaronov.com you can find me on twitter which is abbey maronov or i linked in which is abbey maronov thank you so much for stopping by I really appreciate all these great insights on nonverbal communication thank you so much for having me it's been a pleasure