So, if you look at this particular data, this particular data has a 3 years data, right. If you are lucky with your industry, so you might have more data. So, then it will be easier for you to illustrate, but 3 years data are sufficient to start with the, you know, winter hold model. I have bought a very basic data, so that this complex winter hold model you can understand in an efficient manner. Look at the data pattern. So, this data say first quarter, say April-May-June, first quarter has sale of 108, then next year first quarter, this next year first quarter you can see, these are nothing but first quarter of every year. You can see, look at sales are down, so first quarter, April-May-June, the summer quarter that this product has a low sale, but if you look at the third quarter, third quarter means what? October, November, December, right. So, third quarter to some extent say winter or festival season you can say has a high sale. Look at high sale, third quarter, third quarter every year has a high sale, so that means this data third quarter of every year has a high sale, but first quarter of every year has a low sale. So, that means this data confirms that data has a seasonality. Whatever, you know, look at this first four quarter of first year, then this four and then this four, so this way it is been repeated. So, pattern is known to you and it will be repeated in a similar manner, so that means data has a seasonality, so this is done now. You can draw the graph also here I have drawn, now look at the data has a trend or not. I have taken the overall sales of the data of three years for all twelve quarter and then I have drawn the trend line, look at the dotted line, trend line it has a uptrend also, look at it has a uptrend also, so the data has a seasonality, data has a trend also. So, therefore we cannot use hold model, we have to use, we can do simple seasonal index calculations because that take care only the seasonality that may take care of trend, but they are made by high error, winter method will be a most appropriate for that. So, let us use the winter hold model for this data who is having seasonality and trend together. So, we are going to forecast for the fourth year, for the next four quarter of fourth year what will be your forecast. So, this is nothing but h equals to 1, h equals to 2, h equals to 3, h equals to 4, for this four you know h value we will calculate, like you look at the formula here for this h value, four value of h will make the forecast for the fourth year. So, let us recall this particular formula and illustrate this particular data sets for winter model, now initially what you have to do, initially you have to make the assumption of three smoothing component, say what is that alpha, beta, gamma, look at the initial assumptions alpha, beta and gamma, you have to assume it. Remember here, this value it is the optimum value I have kept here, optimum value I have kept here after optimization of the entire data iterations, initially you can give any value, when I go to the excel I will show you any value of initial value of alpha, beta, gamma you can give not a matter, but at a later stage after iterations all the software will optimize, the solver will optimize the alpha, beta, gamma value for this particular data sets, you will get this alpha, beta, gamma I will show you. Suppose we found this alpha, beta, gamma, so that you can understand the actual iteration effectively, so I have kept the optimum alpha, beta, gamma, but initially you can start with any value I will show you in excel, suppose alpha, beta, gamma we have initialized now or optimized whatever, then you have to calculate the index first, so first year index you calculate 4 quarter as initial assumption, this is also one intermediate steps, actual hold model has not, intermodal has not been started yet, so initial assumptions also you can use for your seasonal index calculation also, so first quarter index will be how much, the actual by the average of 4 quarter, this will be nothing but your index for first year, later in this index will change actually, later after iteration you know this index value will change, but initially you are assuming it that first quarter of first year index is nothing but the actual value by that year all data, all data look at all data of that year by 4 average value, you will get the index for that particular quarter correct look at here, index for that particular quarter, this is also initial assumption to start your iteration and then you can drag this formula, you will get the all for like in a second quarter of 125 by this average value of all 4 quarter, of first year you will get the index of 95 and the third quarter has the highest cell, you can see the index is almost 15 percent extra, so 150 by total average, so you will get 1.15 as the index for that right seasonal index, some of them should be equals to 4, I told you if not then by proportionally you have to do out of 4 how much, so suppose some of them is 4 and weightage, look at fourth quarter also is having high cell, so the 8 percent extra, so these are the initial index for inter method, using the data you can calculate it right, that will change, now let us start the initial level value calculation for first 4 period, you already have the data, so we will start calculating the initial level say L5, for 5th period onwards we will start the calculation, then trend 5, then seasonality 5 and then using these two we will calculate our forecast for 5th period, let us see now the level calculations, how I have calculated the level for 5th period, it is nothing but look at the formula, this is also intermediate steps, so yt of that period by the corresponding period index that which you have already calculated, y5 now for 5th period we are calculating the say intermediate level value, so how I will calculate the level value, effectively what is y5, the y5 is 116 right, actual data, actual data why, because you are calculating the level value right, so this may be down may be up you do not know, in the in your data sets it might be down up it is you do not know, whatever you have to divide, suppose it is here, so you have to divide by the index, so what is the index for that particular L5 quarter, L5 means what fifth quarter right, fifth quarter means what the first quarter, second year first quarter, so first quarter index is 82 percent, so 0.82, so what you do, divide that fifth quarter actual data say 116 by index, what is the index 0.82, so you get the digitalized data level value, so this is what your level intermediate level or fifth period as 140.7, look at here, so any intermediate level also you have calculated now, next the trend, how you calculate the trend, this is also intermittent, final whole inter model calculation has not been started yet, initial assumptions through the process you are doing it, now that trend, what is the trend, trend calculation for the fifth period is nothing but that level that you have already calculated right, intermediate level you have calculated, so level minus the previous period level, this gap is nothing but your initial trend assumption, what is that, the current level that you have calculated and the previous level you have, how you will get the previous level, how you will get the previous period level is nothing but the actual by the index, actual by the index, look at the actual is how much, 141, 141 is the actual by the index is 1.08, so if you divide that you will get the value here, suppose 1, you know some value you will get it here, so say maybe you know it will be 141 by 1.1 means it will be lower right, so some say 138 or something you will get it, so once you will get it here say, say 130 etc you will get, once you get it you will get the difference between them, the level gap is nothing but your trend, so this is what we have written here, clear now, so one that is finalized, let me summarize this part, so it is nothing but the trend, the intermediate trend, what is this, this is nothing but say T5 right, nothing but the corresponding level 5 that you have calculated already 140 minus the previous period the level value, how will get the decentralized value, how will get you cannot take enter 141, 141 by index, so like remember 141 by index, so you will get this value, so this value is coming here, the level gap, current level minus previous level, this is your trend value now, so initial trend also you found, so two value you got the level and trend, you can add them you will get the forecast, so it is index now, but index also you have to calculate then only you can multiply right because here you are doing the inter method, so this part is done now, now we will calculate the index, look at that, how we will calculate the index, it is nothing but the weighted combination, this also intermediate, once these three are done then only you can actually the you know iterative process of inter method will come into execution, so let us see now the intermediate one more component that is called index also let us calculate, so what will be the index for season 5 this one, this one how we will calculate right, so this is nothing but weighted combination, suppose gamma whatever you have assumed you can put 1, 2, 1, say 0.5, whatever 0.2 initially, but later stage you can optimize it, suppose you have taken some say 50 percent or whatever say 16 percent here into the level actual minus level because weighted combination, so what is actual actually 116 and what is your level value, digitalized value of that 116 has gone up, look at remember 116 say 116 were here, 116 has gone up to 140 now, so 116 has gone up to 140, so this 165, this is your index now, 161, 140, it could be less than something, so now effectively you get that index right into that index, this is index actually that index because actual by seasonal, so you will get the index in reverse manner, so this say 50 percent or 16 percent of that plus 1 minus gamma, 1 minus gamma of that corresponding period index, let us see the calculation here, corresponding quarter index is which one, which quarter you are calculating, fifth quarter you are calculating right, fifth quarter index you want to calculate, this you do not know suppose this look at this, I have kept my pen here, this you do not know, suppose this one, you do not know yet, so now you will be calculating this right, so this is which period intermediate index you are calculating, for fifth period intermediate index you are calculating, so fifth period means the corresponding what will be the initial guess or corresponding year, the first year of you know first quarter of previous year, so what is the first quarter, fifth period means the first quarter, so you have to take this as a initial seasonal index, which you have assumed by taking the average of the data, so this is your you know nothing but your initial index and this is the current index, so take the average of weighted combination of them, you will get the index, it might in this case it is matching with the same value, but after once you start the iteration actually it will change, it will not be 0.82, it will change next iteration onwards, initially it might match, so therefore, you are getting this as the new index actual by level plus say 50 percent or whatever of that corresponding quarter index of the previous year, that is your you cannot take the intermediate this index actually, you have to take that index because it is a fifth quarter means the first quarter, the corresponding index you have to take as a look at t minus 6, so fifth means t means t 5, so s 5 minus 4, m is 4, so it is nothing but s 1, so s 1 is nothing but this, so this way you have to take the corresponding index and you will get the index for the fifth quarter now, so you got let me erase now, now you found the index for the fifth quarter also, so intermediate three value you found level, trend and index, now you calculate the forecast level plus trend multiplied by the index, look at the forecast now, level plus trend multiplied by the index, you got the forecast now, now let us see how the sixth period level and trend and seasonal index we are calculating using the winter hold model, the actual iteration of the calculations will come now, so initial value I mean calculated through fifth period, now sixth period onwards we will calculate the actual level trend and the seasonal index and the forecast through winter hold model, so now I have kept the formula here also for your easy understanding, so the first point is the level, so we will calculate the level value now, how we will calculate using the this formula we will be using here, so L6 say because sixth period calculations will be done now, so for L6 is nothing but alpha of sixth period actual by the index we have already calculated the index we have significant amount of index now in our hand, so now we will use this index in place of that though it is same but we will take that but other for other three we will take the older one the initial value one, but for the first fifth quarter we will calculate this like you know first quarter of every year we will take the revised you know index now, but now let us see which one we are calling here now, so L6 nothing but the level value for the sixth quarter is nothing but alpha into the actual value the decelerized value what is the decelerized value Y6 what is Y6 134 by index what is the index you are at T6, so 6 minus 4 means S2, 6 minus 4 means S2, 6 minus 4 this is nothing but S2 what is S2 0.95, so 0.95 as S2 you have to take here look at here S2, so Y6 means S1 134 by 0.95 look at here this I have called here 0.195, so this is here say 86 percent of that plus 14 percent 1 minus alpha of you might say first how come you got 0.86 I will show you later through optimization do not worry initial whatever you assume no matter once you finalize the optimum value you will get this value, so suppose this alpha of this plus 1 minus evaluated combination of the previous previous forecast what is the previous previous forecast level plus 10 level plus 10 you have to take decelerized value you have to take index you cannot multiply, so here level what was 140 plus a 9.7, so this value level plus decelerized value because this is all decelerized forecast level value the trend line value base value we are calculating right index you cannot take here rather you have to divide the actual by index, so that only decelerized that in between line that you get the data base value, so 86 percent of that plus 14 percent of the previous level plus 10, so you get it this if you take that sum you are getting 141 this is your forecast for the 6th period, so that forecast is done now now intermediate level similarly calculate the trend look at that is done now now go to the similar way we calculate your trend how we calculate the trend throw inter method this calculation you take, so you are calculating the t6 right t6 you are calculating how we calculate beta say 50 percent or say 78 percent here we found say 50 percent 50 percent of the level gap new level you already found right 141 minus 140, so that level gap but you cannot take only that say 50 percent of that plus 50 percent of or say 22 percent of the previous trend same logic like the hold model we are not changing anything in trend model, trend formula it is as it is 50 percent of the level gap say here 78 percent optimum beta plus 22 percent of the previous trend you will get the forecast for the trend as it is very easy done now if you drag it you will get because this formula is the final formula look at this these two are now the optimum formula look at this these two are now the optimum formula if you drag them in excel you will get the entire inter calculations now index also one left one part is left right index calculation like this this one this one, so let us go to that part now look at the index now seasonal index for which period for 6th period we will calculate how come look at it is also 0.95 you might be confused or it is also same coming same no no no after some iteration all this will change you will get to know, so suppose how will get this value now gamma suppose 16 percent or 50 percent say 50 percent of the actual by level, so index you are taking the index the reverse value you take actual how much how much 134 and what is your level 141 you take that division you will get the index that index also 16 percent of that plus 1 minus gamma or say whatever multiplied by the corresponding quarter index S6 means what second quarter second quarter right second quarter means where is the old index old index you have to take 50 percent of that and 50 percent of current period index now, so current period index you have already calculated 134 by 141 and say 50 percent or say 16 whatever optimum value you have multiplied plus weighted combination of that 1 minus gamma of S6 means the second period second period index is how much this second period look at second period index is this much, so that you take here will get the index weighted combination of C null index now that you keep here done through winter method now we have calculated based on the initial assumption or initial calculation process. Once you get the these three value level trend and the index once you get these three value look at level trend and index you calculate the forecast now this plus this multiplied by the index look at here you found the level for sixth period you found the you know trend for sixth period you found the index now, so if you add these two and multiply the index you will get your final forecast now for that sixth period here we have done it we look at here, so level plus trend multiplied by the index the new index that you have found, so this data you will get the forecast for the sixth period using the inter hold method. Now what you have found you actually found the look at for sixth period the level through inter method the trend through inter method the C null index through inter method and the final forecast. Now if you drag it all this you drag you will get the forecast for you know the calculation of inter hold model data and the forecast value for all the intermediate data sets and the corresponding forecast also but that is not final final forecast will come here for the fourth period. Let us see the iterations now, so here is the final iterations you could drag them so far I have shown up to this up to this up to this and this right now this formula you drag this because this is the initial calculations this may not match. So, this is the final formula through inter method you drag them you will get the forecast in excel also. So, you got the forecast for data now now look at this level and this trend and the index this index are fine look at this index now look at the plus 4 index now it is not the same look at to some extent because you have a limited data. So, it is not changing here at least this one 8.82 it change to 0.83 now it is not the same it is 0.83 now you know over a period of time it might change also. So, therefore what happens if it is remains some what a matter not a matter ultimately you are getting that index from the beginning itself. So, suppose but that may not be final because you are calculating the index through iterations and data are changing. So, therefore this index also will change suppose here we have limited data if increase the data sets we will see the changes in the you know index also. Suppose here we found the final value and the corresponding index now you calculate the forecast this error part I will discuss later. Now, let us focus the forecast final year 4th year forecast in inter method now age will come to the picture. So, what is the forecast for first period now 13th period it is nothing but level what is 152.29 say plus trend what is 3.40 what is age first period you are developing. So, age equals to 1 now age age is 1 here 1 here now plus age into you know trend multiplied by the index what is the index first period index what is the first period index first period index is nothing but 0.83 you will get the forecast as 0.28.50 done now for the second period suppose 13th period you have calculated now for the second period of 4th year that means 14th period how will calculate the 14th period 152 as it is 0.29 plus age equals to 2 now into trend as it is strong trend 3.40 3.40 multiplied by the index which index you will calculate now you have to take corresponding index 0.95. So, 0.95 we will get 151.45. Similarly, for you know for third quarter you multiply this with age equals to 3 this for age equals to 4 age equals to 2 age equals to 1 you multiply this you know trend with the level and multiply the index you will get the forecast for this age value I have mentioned here here and you will get the forecast for the next year how much forecast 128, 151 and 157 look at after again you are multiplying the index right. So, that you know get the zigzag pattern. So, suppose you got the trend line and after that you are making again zigzag. So, that you know top down pattern come back. So, seasonal index pattern come back. So, this is what the winter hold model you have to see the forecast look at here look at for third quarter we have seen that every year third quarter has a high sale look at here every year third quarter has a high sale look at the winter method also whether it is following the trend or not seasonality pattern or not look at the third quarter highest sale 185 you will not find anywhere. So, highest then again in fourth quarter it is down 178. So, it is down now. So, that means it is following the trend as well as the seasonality also. So, therefore, winter method is very strong and popular when you have the trend and seasonality here you can see the you know formula here look at here. So, age means 1, 2, 3, 4 particular additional period that you want to consider and this is nothing, but the index in which period you are considering you put the value of age and m, m is 4 fixed you will get the corresponding index that is the last index that you found that you calculate and multiply and you carry forward the forecast. Now, let us go to the excel and understand the entire calculation of winter method. So, we have come to the excel now and if you see the column number b it is nothing, but the quarters we have 3 years data which I have also illustrated in the PPT now that was the screenshot of this excel actually, but if you see here we have 3 years data and say 12 quarters data we have and we have to forecast for fourth year that is 13, 14, 15 and 16. So, this 4 years you know 4 quarters data we will predict now using winter method. Now, these are the actual data you can see that the data I have drawn the pattern of the data here also you can see the blue color data which are you know actual data and it is seniority and to some extent 10 is also there which I have shown you earlier. Now, first step remember the PPT that I have shown you the steps first you calculate the index initial index. So, that is here you can see 108 by the average of first 4 quarter. So, this is the index initially assumption of index for quarter one. Similarly, we have subtract the average and the ratio that second quarter index is 125 by the average and these are the 4 index we have calculated right first step. Then next the initial value assumption for level what are them for level and then for trend and seasonality for these 3 level you can see level then trend and then seasonality right. So, these 3 part we have to calculate as a initial value. So, let us come to the level first initial level how we have calculated we have calculated the actual we have taken the actual data of 5th period from 5th period onwards we will start the calculation. The actual value of 5th period by the index of first quarter because if 5th period nothing but a first quarter first period. So, here you can see the actual 116 5th period actual data y by what is that it is nothing but y by index right. So, here it is y5 by index say 5 or you can say that you know I 1 1 here because you know first quarter and 5th quarter are same. So, this we have done look at C6 by F2. So, this is nothing but the index for that quarter. So, if you calculate 140.70 this is the initial level assumption look at here. Now, let us go to the calculation of the initial trend. So, how I will calculate the trend? Trend this is the initial not the actual model of trend winter model has not been started yet initial assumption of level trend and seasonality required.  What is the previous period level? Previous period level is nothing but 140 by index 1.08 that means the gap between current level and the previous level. So, that we have taken as the initial trend right look at here this is nothing but 140 minus 141 by 108. So, this is what 9.7 whatever it is coming the initial trend then the seasonality also index also you have calculated. Let us see how come we have taken say 50 percent weighted say I can see you like you know say whatever weightage I have given suppose 1 here initial value not a matter look at this value into the current index what is the current index that as per the current data 116 by 140 the level you found if you take that gap 116 by 140 you will get the index but that takes a 50 percent of that or whatever 100 percent whatever you put this is alpha beta gamma or initial level I have taken 50 50 and 100 you can change this automatically it will be optimized do not worry.  So, therefore, it is coming to be 0.8 but if you change that gamma optimize it might change also right. So, now this is the three value let me put color these are three initial assumption of level trend and seasonality right. Now, we have done one level of iteration, but the basic level of assumption you can say one way of assumption and then the corresponding forecast is L plus T whole multiplied by the index. So, we got say 124 whatever. Now, first iteration of winter method will start look at here how come we found this alpha into level value plus 1 minus alpha of previous forecast. So, what is that you have to look at you are calculating the level. So, actual value you cannot take C7 you cannot take what is C7 C7 is nothing but the value of sixth period actual data by the corresponding you know the index that what is the corresponding index look at here the corresponding index is now F2 it is F3 because you have come to second quarter sixth quarter means second quarter now. So, you have to take corresponding index of 0.95 as the second quarter index. So, you divide that you will get the level value of that particular quarter intermediate level plus 50 percent say you have assumed 50 percent say initially 50 percent of previous period forecast. So, level plus trend like D6 and E6. So, level plus trend that is 50 percent of that. So, two level weighted you are taking weighted average. So, you found this as a forecast for you know level. Now, similarly trend you can calculate the trend beta into the level gap 145 and 40 that is the gap beta say 50 percent plus 1 minus beta of previous trend what is previous trend 9.70 look at here. So, this way you can also take the weighted combination of the trend. So, trend is done now seasonality index now you have to revise it. So, what will be the seasonality index? It will be the gamma combination weighted combination of gamma with current level values and the corresponding seasonal index plus your old index seasonal index. So, how come you can do it? Look at here. So, here it is nothing but C7 by D7. C7 is current value actual and you already got the level 145. So, if you take that you will get the you know index the current index seasonal index. So, that but gamma percentage of that plus 1 minus gamma of the corresponding quarter index the old index. So, weighted average of that is your forecast for next you know index revised index for second quarter. So, here we found 9.92 it was 9.95 here it is 9.92, but you do not know what is the optimum value because alpha beta gamma is the initial assumption right these are our initial assumption we will optimize it then we will get to know. Now, since you found all these three now now what you do look at the forecast level plus trend multiplied by the index. Now, if you drag all them this from this here onwards if you drag the process you will get your forecast right you will get your level forecast you will get your trend forecast you will get your index forecast. Similarly, you can do and also you will get your overall forecast right done. Now, once it is done. So, look at the final level value and final trend value the best trend you found level and trend using that by h term multiply with h term you will get to know the final forecast for the fourth period. So, what will be the fourth period forecast look at h equals to 1, h equals to 2, h equals to 3, h equals to 4 we have mentioned here right not the index these are the values h. So, I have written here only. So, the fourth period 13th quarter forecast will be level plus h into h into trend h is one first period multiplied by the index you will get 133. Now, for second period suppose for 14th period. So, 14th period what will be the forecast level say point something plus h is 2 now into trend 2.89 multiplied by the corresponding index. What are the index corresponding index you found here corresponding index you found here 0.93 this way you will get 152.45 say. So, this way for first one you have to multiply the corresponding index not that index it is for fourth quarter index 1.05, 0.83 is the index for the first quarter this way you multiply with h time of the trend plus level multiply the corresponding index for that final index that you found you will get the forecast for all four period. This is what you know outcome of inter method, but one thing that this value we found are not the best 133.152.182 are not the best because this is based on this initial smoothing parameters assumption. Now, let us optimize I have also calculated the error based on this data means the initial guess I have calculated the error I have calculated the absolute error and MAD and say square error and MSc and RMSc also. Now, look at the current RMSc 7. something right current RMSc 7. something. So, let us optimize it go to data go to solver I have put all the data here. So, I do not need to repeat that again. So, I have to minimize the RMSc. So, RMSc I have called here as the objective function it is a minimization problem. So, I will select the minimization cell and my changing variables are the decision variables who are alpha beta gamma right look at alpha beta gamma are my changing variable then condition all this condition are nothing but you know you can add the condition here conditions are nothing but this condition this all these variables should be less equals to 1 less equals to 1 and this should be greater equals to 0 I have already written them here. So, 1 I can delete no need to repeat that you put not an issue but it is a RMSc is a nonlinear function. So, we will select the nonlinear value as the optimization process makes sure that you click this because nonnegative solutions we are required we are planning to get the nonzero solution. So, non negativity conditions you have to click now if you solve it you will get the best RMSc least RMSc and the best alpha beta gamma also look at the changes in alpha beta gamma. So, here we found the best alpha beta gamma 0.86, 0.78, 0.16 and the RMSc is 2.66 and the corresponding final forecast is this look at here 1.66 you can delete this now look at 1.28.5, 1.51, 1.85, 1.70 look at the pattern of the data also it is also following to some extent you know cnality look at here. So, 1.20 is the first quarter forecast look at here if you copy this data and if you paste here you will get the pattern of the data look at here. Now, if you see 1.28 is the 13th period forecast look at here now 1.28 is the 13th period forecast which is nothing but first period of fourth year look at fifth quarter and ninth quarter look at the trend uptrend, but it is the lowest among the quarter data or for that year look at 15 period that means third quarter of fourth year highest sale 1.85 which is higher than 1.60, 1.50. So, it is following the trend and the cnality also look at it has a highest value. Now, if you look at all this data and look at the forecasted graph now with the sales look at here we have started our forecasting from this period say from here onwards. So, from fifth period onwards we have started our forecasting and look at the pattern of forecast also it is matching with the actual data pattern whatever the past period data you have now the forecast are also in same line. So, you can see here. So, this is what the beauty of winter method it takes care of the cnality and trend and if you look at the data pattern it has uptrend also. So, it is following the uptrend it is also taking care the cnality also look at the pattern in third quarter it has the highest sale it is also taking care also and also first quarter it has the lowest sale 1.28 lowest sale is also taking care and again fourth quarter it is down. So, it is following the pattern it is following the pattern. So, this is what the winter method. Now, let us come back to PPT now here. So, this graph same graph I have drawn here as the illustration of winter hold method. This is all about winter method, but now I will have to share one additional information for you that. So, for whatever the procedure of winter method we have discussed we call this a multiplicative method of winter's method right winter's hold method. There are two way of analyzing the winter hold method. One is the multiplicative method like you know level plus trend you add level plus trend per each times of trend part then you multiply with the index. So, this is called the multiplicative procedure of winter's method or winter's hold method and we have illustrated detail on. There is another process called the additive method of winter's hold method almost similar process similar calculations. You know this excel sheet I will share you can also practice at home what the formula will have to change only like notations concepts all will remain same only thing is that here you can see you are not dividing the index to the actual data. So, you are subtracting the index value which is very less closure to 1 right may be less than 1 or greater than 1, but closure to 1. So, that index you are subtracting not dividing you are decentralizing this way actually not by. So, this is not that popular this one is popular therefore, I have illustrated it which is easier to understand because you know the actual data you are dividing by the index or decentralizing the data you are bringing a trend line right. So, therefore, and that will be your level value similarly here same information are there same ingredients are there, but you are not dividing you are subtracting the trend sorry index from the actual value rest all are as it is trend calculation will be the same in index also when you calculate the index you are not again dividing the actual by the level you are taking the subtraction. Therefore, here also you are adding to the data not you are multiplying not here multiply here you have multiplied here you are not multiplying you are adding to the level and trade each time of trades plus the seasonal index that is it rest all are same only here you have to subtract here you have a division here you have a division again by click out it is a reverse of the you know index and level. So, therefore, here you are subtracting here actually you divided actual by level you are getting index, but here you are subtracting. Therefore, in the final calculation also final forecast also you have to add the seasonal index, but not the multiplication here you have multiplied with level plus 10 here with level plus 10 you are adding it that is it this is what the additive version of hold model. You can practice that with the data that I have shown you can change the calculation process and you can practice this also as a part of additive version of hold method, but multiplicative method is sufficient to you know get into a inter-method and application in the industrial problem. Now, whatever model you can select whether additive method or multiplicative method the essence of both concept is that you actually take care the trade and seasonality of the time series data and you make the forecast with the appropriate you know pattern of the data. What has happened in the past you are following in a similar manner and you are making the forecast for the future in a similar trend with similar seasonality component. This is what the winter method I believe it is clear to everybody. So, let us you know close this winter method session here. In the next class we will focus on multiplicative decomposition method which is alternative to winter hold method remember another concept we will be discussing which is very Lehmann way of you know people can understand that also and industry also prefer that. That method we will discuss in the next session which is called multiplicative decomposition method and this type of all calculations of winter method are not required there in a easy manner you can also understand as a backup of or alternative process of winter hold method. So, with that let us conclude the winter hold session. Thank you.


Just been doing a bit of traveling today, drove for a few hours through the jungle. I will have some pictures and videos on Instagram very soon. My Instagram is Naxiva YouTube, now I'm just at this lake and got a great video for you today when the narcissist knows it's all over. When they know they don't have a chance, you're no longer susceptible to their manipulation. You're no longer under their spell. They can't pull the wall over your eyes anymore.  And when that happens, they're not even going to bother trying to look for you. They're not going to bother love bombing you or trying to come back. Because now they know they haven't got a chance. And when that happens, they're just going to claw to destroy you behind the scenes. They're going to try and tarnish reputation. They're going to say horrible things about you to other people. They're going to try to discredit you, to smear your name. They're going to enforce their flying monkeys to come after you and do their bidding. And if they haven't already, they may start stalking you. So you may find them watching you at your house or your work. Or they may just be stalking you on social media. Because at this point it's very different to any stage before this because now it's hit them. They really know that you're not coming back. They know you're gone. They know that you're not going to see them again. They know they haven't got a chance anymore. So they just want to put the final nail in the coffin. They just want to finish you off completely and leave you to rot. Because that's all they're going to want to do once you cut them out completely. They're just going to want revenge because they take it as rejection. You don't want anything to do with them anymore. You see they don't look at the things that they have done to you that made you no longer want to deal with them. Because it's not like you're just this cold-hearted person who just randomly and for no reason cut them off and doesn't want to talk to them, doesn't want anything to do with them. No, they did things that they knew you didn't like. They consciously intentionally and deliberately harmed you or tried to harm you. So you are justified in leaving them and not wanting any further contact with them. You are completely justified in doing that because they have no intentions of changing. They're not even looking at what they've done to you. They just point the finger at you, they're blaming you for everything. And then when they know it's all over, they're coming back and they want to revenge. They wanted to punish you. They wanted to harm you even more. Which really makes no logical sense. But as we should know by now, narcissists are not logical creatures. Everything they do comes from their own unstable emotions. Which is why they come across as very irrational. A lot of the things they do don't make any sense. It doesn't add up. There's no justifiable reason for why they're doing what they're doing. But yeah, that is what they will do. When they know it's all over, and you do need to prepare for that when you do go no contact. Everyone talks about going no contact. Everyone advises people to do that. And I'm not saying you shouldn't, but you do need to be aware of the risks. Because going no contact, it's difficult enough. And it's so, if you feel connected to this person, but not only that, it does come with consequences. It does come with unwelcome and unpleasant effects. So you need to be aware of that and you need to prepare for it. Because they're not just going to let you go so easily. They're going to make it difficult for you. They're going to want to punish you. They're going to want to make you regret your decision. And that's why I wanted to make this video today, to just make you aware of that. And to make you better prepared for it. I want everyone to be safe. I don't know, it's difficult when you're dealing with narcissists. Cars are very dirty. Been driving off road a lot. Let's see what we got in here for the dogs. I always like to carry some treats around dogs and the cats as well. But it's sad because sometimes they just run away. And then I try and throw a treat at them and they think it's an attack. Let's see if he takes this. This dog seems quite friendly. There you go. Only one. Whoa. You see what I mean? What's going on? It's like they're afraid of it. I don't want to hurt you. I'm just trying to help you while you're running away. I've got a feeling that someone really hurt this dog. Because that's what happens with animals, humans too. You can come to the dog and try to love it, but it's just confused. It's very confused. It doesn't know how to respond to real love and affection. It's very sad. It's sad for me too because all I want to do is just give love to these dogs. That's why I went out and put these treats, but they won't even take them. And these dogs must be starving as well. They're running away. Come back. I just want to love you. I shouldn't laugh really. I mean, it's not funny. Well, it is in some ways, but. In some ways, but it's also very sad as well. Now, what am I supposed to do with these treats? I can't eat them. I think there's another dog down here. Maybe this one will take it, or maybe it's going to run away like the other two. Let's see what happens. As long as it doesn't attack me, we'll be okay. Yes, I think this dog can receive the treat. He didn't look too sure about it at first, but he's given it a go. He looks very suspicious. Still got one left. There's no more dogs nearby. He's trying it. 59 live viewers on here right now on the Narc Survival Channel. They're all watching a stray dog eat a treat. Something very unusual and different. But there we go. Yeah, as someone said in the live chat earlier, this is a perfect example of abuse. And also how it affects us as narcissistic abuse victims. Because some of us, some of us, once we've been through it, it doesn't matter if it was the perfect person walking the earth, came into our lives. We wouldn't be able to receive their love if we haven't healed. But then those of us who have moved on, like that dog there. Yeah, we might be a little bit suspicious at first, but at the end we can still receive it. So that's something for you to think about today. Which dog are you? I don't know about you, but I'd like to be that last dog there. There he goes. He's got the treats. He's enjoying it. He's having a good time. It's all good. He got what he wanted in the end. But unfortunately for the other two dogs, they were a little bit distrustful. So they ran away and they left hungry while this dog got it all. That's just how it goes sometimes. But yeah, when the narcissist knows it's all over, be very cautious because you don't know what they might do. But one thing's for sure, they're going to try to get revenge in some way. They're going to try and punish you. So be aware of that. Protect yourselves. Stay safe. Thank you all for joining me on another Knox for a live video. If you enjoyed it, please give it a thumbs up down below. Let me know your thoughts on the comments. Is it all over for you? And has the narcissist tried to punish you or get revenge? Let me know. I read your comments every day. Again, thank you all and I will talk to you in another one very soon.


Hi and welcome to the session. I am Pika here. Let's discuss a question which says show that the given differential equation is homogeneous and solve it. As d y by d x minus y plus x sin of y over x is equal to 0. So let's start the solution. The given differential equation is x d y by d x minus y plus x sin of y over x is equal to 0. Let us get this equation as number 1. Or this can be written as x d y by d x is equal to y minus x sin of y over x. Or this can be written as d y by d x is equal to y over x minus x over x sin of y over x. Or this can be written as d y by d x is equal to y over x minus sin of y over x. Let us get this equation as number 2. Now right hand side of the above equation or equation 2 is of the form g of y over x. And so it is a homogeneous function of degree 0. Therefore the given differential equation that is the equation 1 is a homogeneous differential equation. We will solve equation 2 by substituting y is equal to v x. So for y is equal to v x. Therefore d y by d x is equal to v plus x sin of d v over d x. Now we will substitute the value of y and d y by d x in equation 2.  Now on separating the variables we have d v over sin v is equal to minus d x over x. By integrating both sides we have integral of d v over sin v is equal to minus integral of d x over x. Or we can write the left hand side of this equation as integral of cosecant v d v and this is equal to minus integral of d x over x. Now the integral of cosecant v d v is log of mod cosecant v minus cot v and the integral of d x over x is log of mod x plus log c where log c is a constant of integration. Or we can write this equation as log of mod cosecant v minus cot v plus log of mod x is equal to log c. Now by replacing y by v x or v by y over x we get log of mod cosecant y over x minus cot y over x. Plus log of mod x is equal to log c or this can be written as log of mod cosecant y over x minus cot y over x into mod x is equal to log c. Now this can be written as log x into 1 over sin y over x minus cos y over x over sin y over x and this is equal to log c. And this can be written as x into 1 minus cos y over x over sin y over x is equal to c. And this can be written as x into 1 minus cos y over x is equal to c sin y over x. Hence the general solution of the given differential equation is x into 1 minus cos y over x is equal to c sin y over x. So this is the answer for the above question. I hope the solution is clear to you and you have enjoyed the session. Bye and take care.


Today we're going to find out which I as one member will teach me the choreography for the lift up. Ah heck yeah, you expected something different, oh hell nah, today we're going to be doing the quiz and maybe if we do this quiz we might do another quiz because I don't know what we're going to be doing because you know that's what we do on this channel because I don't know man, I just thought of doing a quiz today. So yeah, let's just do this. Okay, now before we do the quiz, let's get out in a bias heart ready, it's an ace. Um, is that an ace? I don't know, that's a spade. I don't know, I can't remember what the cards are. By the way, doofies, should this be our hand sign? You know like if we either meet we could just like do that as the hand sign. I don't know, I don't know but should it be a hand sign, I don't know. Anyways, so today we wanna, we, we, we, we, we, we, we, we, we, we, we, what we wanna do is first we wanna find out which member, well actually we wanna guess what member we want to teach us. I would love if Chey won, I thought me wouldn't do, but I think Chey won's now becoming my bias, like full one bias, I'm sorry to him, I'm sorry to him but it's just becoming one Kim and it's Kim possible. So yeah, let's just do this and here's the first question. If you were a part of Produce 48, what rank do you think you will be? Now I'm gonna be perfectly honest, I don't know. But actually I do know, I know that I would not be in the top 12, because I'm not that good at anything. But if I could, I'm gonna say, I was better than two people. Okay, okay, that's all I'm gonna say. I don't know who, but whoever you guys were that I was up against, I'm good, but I'm better than you, you know? Which position would you prefer if you were in a K-pop girl group or just a K-pop group in general? Now, I think I could be a good leader because I'm like, yo, knew that, cleaned my shoes or not. Actually now that I think about it, I probably wouldn't be a good leader. What about dancing? We all know that I could dance, I could do this, and I could do that, and I could do that, and then I could do that. So we're pretty good at dancing, but vocals, do you wanna hear my beautiful voice? Oh, beautiful, so beautiful, I loved it, the pieces.  And my rap skills, do you wanna hear my rap skills?  Ooh, maknae with a beard. I think so, that could work. And then visuals? Not really, I don't have visuals. But, I mean, this is actually kind of hard. Okay, what if we just do this? I don't know what one I chose, what one was that? I think I chose rap, I think I'm a rapper. I'm watching you, just like how Chaewon is watching us. It's like, she's watching me, watching you. If you were a K-pop idol, what events are you excited for the most? I'm not sure if that's exactly what the, what events do you look forward to the most? That's basically what I said, but I put more emphasis into it. Whoa, I used the big word. So, would I look forward to the most? A solo concert, a fan meeting, a music show promotion, or a fan sign? Probably, probably a fan sign, you know? My legit thing about it, like, you know, signing stuff for your fans and all that stuff, and then like doing stuff for your fans when you see them in person, that is pretty cool. The day I met a fan in real life is the day I'm gonna freak out. Like, we're both gonna be freaking out, okay?  Ooh, let's take a photo, it'll be like that. What kind of bed do you prefer in a comfy one? Single bed, ooh, I cannot do that. I cannot, I just cannot. A queen-sized bed, that I can do. King-sized bed, is that bigger or smaller than a queen-sized? I don't know, it gets too confusing. And then a double-decker bed, that's like, is that like a bunk bed? That's what we call them here in New Zealand, you know? Like, one here and then one up here. Is that what a double-decker bed is? Now I wanna know. Oh, so it is a bunk bed. Whoa, this one's got a slide, that's pretty dope. Not gonna lie, that's pretty dope. If my one had a slide, I would probably do that. Another one with a slide. Okay, this one's actually pretty cool.  Yo, I am low-key liking this. I might do this when I'm gonna buy, build a house or whatever. I'm gonna do that stuff. Holy, whoa. That's a triple-deck bed. And then there's a hamper underneath. Whoa, whoa! Okay, I'm getting too much into a double-decker bed. I'm gonna call them that now, because they just sound so much cooler than a bunk bed. Ah, a double-decker bed it is. I would have gone with queen-sized, I'm pretty sure that's what I got, but double-decker? Okay, so this question is something that I actually wanna do soon. So which hair colour would you like to try one day? If there's red, I would like to try red. Maybe even the colour red that's showing right here. Something like that, or maybe a bit darker. You know, something like that. I think I could look cool with it. Anyways, if we go down, let's see if there's red. Brown, brown, black, pink, mint, purple. So we're gonna go for the closest one, which is pink. Which entertainment company would you like to enter as a trainee? Ah, for sure, FNC Entertainment. There we go. What Korean food would you like to try the most? I don't know, that's a good question. The dog, dog, dog, bokeh? Kimchi pancake, I've had that before. It's actually pretty decent.  As you know, I think I do know. I think that's like blood sausages or something like that. Bibimbap, that's like the sushi from Korea, but it's called bibimbap. I think, I don't know. I know bap means rice. Then jang, jang, myon. I've seen that a lot in Running Man. I think there's like cold noodles or something like that. And then kimchi fried rice, I've had that before. So like, basically the only one I don't know is the dog, bokeh. Hot and spicy rice cake? Nah, I don't like rice cake. Oh wait, actually I'm gonna confirm if sundae is blood sausages. Yeah. Now then, it leaves us down to this. Which places in Korea would you like to visit? Ooh, Han River. Han River, if Han River's in here, 100% gonna go with it, but we'll still read the other options because that's what we gotta do. Namsan Tower, don't know. Han River, do know. Actually I think I do know Namsan Tower. I think that was like in the second or third episode of Running Man. And they had that comedian, and I don't remember that episode really well. I'm gonna confirm if that's it. It's scary how correct I am. I know she's like a comedian and all. And it wasn't like the second or third, it was the sixth episode. I remember, I remember, oh my God. Yo, that was so good. I need to rewatch that episode. Definitely when they were doing like that run with like the cups and all that stuff. Yo, that was, oh dude. I love the early episodes of Running Man. The Yongbok Palace, don't know. Gangnam Underground shopping street. That actually sounds pretty cool. Lottie World? No. Hongdae Club? No, we're going with Han River. We got her! Holy Cremoli, we got her! We got Kim Chae Won. My bias gonna teach me how to dance now. You did not know that Chae Won was such a lovely girl until you met her. She was very friendly and told you that she could teach you the choreography easily and just follow what she did. In between, Chae Won would notice that you have had a hard time following and suggest to take a short break before continuing. That's so what she would do and that's so much of what I would do. I would be failing and she'd be like, yo, just take a short break dude.  Just take a short break and then calm down and come back. And I'd be like, oh, thank you for being so happy. Wow then. That just happened and that was freaking sad. What are you doing? Let's see if you can get your biases. Comment down below who you got because I got Kim Chae Won. Are you watching my bias? Legit, I am freaking, I am happy about that. I am happy about that. I am swag. Look at this 20 year old guy fanboying over getting his bias in a group from a quiz. Nah, but thank you all for watching this video. I hope you guys did enjoy. If you guys did, show some support by leaving a like and comment down below who you got for your bias for the quiz. And also there'll be a link in the description down below towards the quiz so you can do it. So yeah, thank you all for watching. I hope you guys have a great day and just keep on smiling. And adios my doofus.