 Hello everyone, welcome to the class of business forecasting. Today we will discuss exponential smoothing. In the previous session we discussed different type of moving average methods. And under moving average methods we discussed simple moving average, weighted moving average and exponential moving average. And we illustrated them with practical examples and using excel also. Today we will extend the time series data to a different model that is called exponential smoothing. It has a different structure of you know modeling which is different than moving average. I will give you the description of that and also the different idea between what extension we have been doing or we are doing in exponential smoothing as compared to the moving average also. That also I will discuss and then we will illustrate the concept, the technical part of exponential smoothing and also the excel illustration. So what is exponential smoothing? In exponential smoothing we actually assign the weight to the data exponentially. And initial period are given maximum weightage and then that will optimize and then the weightage of the remaining period will be distributed in a exponential manner. Slowly it will reduce. So that means we give higher importance to the immediate data. That importance or the parameter we call it as smoothing constant. So there we have to optimize that smoothing constant we call it as alpha say which lie between 0 to 1. So that means how much weightage you want to give to the immediate period. And in exponential smoothing we give highest weightage to the immediate period. You can see here that that means that the recent data points are given more weightage compared to the older one. But exponentially the weightage element reduces or decreases to the past observations. But theoretically you consider all the past data in your you know process of averaging and forecasting. But since the weightage are been decreasing in a exponential manner we consider all the past data we call it as exponential smoothing method. And you know another assumption is that data should be stationary. If you have a stationary data where the mean does not change over a period of time standard deviation it remains to some extent steady. It is better to use exponential smoothing model or exponential smoothing model actually works very well with better accuracy or measure of accuracy. And the alpha range lies between 0 to 1. And when it comes to the exponential smoothing model there are three you know different models are there. First is the simple exponential smoothing which we are going to discuss today. And then we can extend that with more different type of data pattern like we have discussed in the components of time series session that data can be seasonal, data can have trained also. So, in that case there are different methods of exponential smoothing. If you have a data which is having trained up trained or down trained in that case you can use hold exponential smoothing. If data has a seasonality and trained together in that case you can use the winter's hold method or winter and exponential smoothing. In the forthcoming session we will discuss these two concepts in detail. But today we will consider only simple exponential smoothing and how it is developed. So, let us see. So, as I mentioned that you know it gives some higher voltage to the immediate period and slowly, slowly exponentially the weightage are going to reduce or decrease to the older period. So, calculation of the forecast are nothing but the weighted average of the immediate data and the forecast of the smoothed forecast of the immediate past period. So, how come it is been developed? Just now I am talking you might be confused that you know just now I talked about it is exponential series. It takes care of all the past data, but the weightage are been reduced in a exponential manner. It is decreased, but theoretically we consider all the past data whereas in moving average we consider the fixed amount of data. For example, suppose if you have a data like this say Y1, Y2, Y3, Y4, Y5, Y6, Y7 like this dot, dot, dot. So, suppose if you take a three period moving average, so three period moving average is fixed. You make the forecast for Y4 higher. Similarly, when you go for Y5, you drop Y1 and you consider Y2, Y3, Y4 and you forecast Y5. So, this is what you drag the moving average. So, three period are fixed now every time you are carrying forward, but all the period you are dropping and new period you are adding right. These are the moving average, but in exponential smoothing actually what you do? In exponential smoothing actually you do not take the simple average of couple of past data. You actually you know suppose you are forecasting Y5, you take the weighted combination of the all the previous periods and you give a maximum weightage to the Y4, alpha weightage to the Y4. Similarly, if you go for the forecast of say you know for the forecast of say Y7, suppose you want to make forecast you actually take all the past period and where you give maximum weightage to the Y6, alpha. So, this way theoretically you consider all the period in your exponential smoothing process. This is what the difference between moving average and exponential smoothing. Now, let us see the formula of exponential smoothing. If you look at the general formula, so alpha weighted you give to the immediate period. Suppose you are at Y7, you want to forecast for Y7, so Y6 you are giving alpha weightage right. That you have to optimize, look at this point. That you have to optimize and also if you think that you want to give more weightage to the immediate period. So, you can increase the alpha value. If you want to give less weightage to the immediate period and you want to give importance to the older period, in that case you can give some sort of lower weightage to the immediate period and you are giving importance to the older data and you can also distribute the weights to the older data also. I will show you both examples today. But now suppose imagine that we will optimize the alpha. So, initially you are assuming some value as alpha say here we have given alpha and here the first period weightage is alpha. Total weightage should not cross 100% right. So, alpha say 20% or 50% so alpha you have given the rest of the weight. Next period the weightage will be alpha into 1 minus alpha. Second will be alpha into 1 minus alpha square then alpha into 1 minus alpha cube. So, these are plus dot dot dot. So, this way you are actually spreading the data sets with exponential weights and all data, first data of time series you are taking into account and you are making for the next period. This is what exponential smoothing model. But in general you can write that in a short format like this. The first period forecast and alpha into the error term of that period. Suppose for example, suppose you want to make forecast a Y7 just now I talked about Y7 equals to Y6 forecast plus alpha that weights of 20% weightage you have given to the immediate period say alpha into the error term say Y6 minus Y6 hat. So, this is your this is the error this is error term. So, forecast of previous period plus alpha into error term. So, this is the general structure if you club this entire formula and you can create a generalized formula in a iterative process it will come up with this forecast. This you can let me illustrate that how actually this formula can be derived from here or other way this exponential series can be derived from this cluster formula, club formula let us see. Suppose here I have written same formula again how this is derived or this has been developed through this formula or other way I will discuss that now. Suppose if you look at the screen here. So, if you see here this formula as I mentioned the previous period forecast plus alpha into the error term this is the error term right this is the error term. So, now this I can illustrate like this weighted sum also alpha into actual plus 1 minus alpha into the forecast. So, that means say Y7 I was talking about Y7 say. So, alpha into Y6 plus 1 minus alpha into Y6 hat simple way it is easier to understand. So, this is nothing but the weighted combination of the previous period actual and forecast this formula I will keep in excel and I will show the illustration in the numerical example. So, rather than this formula I will prefer this formula because it is easy to remember. So, let us see this formula. So, how we can derive it? So, we can write like this right now let us come here. So, if you see this particular formula this I have written as alpha into this Yt alpha Yt plus 1 minus alpha Yt hat just I have rearranged. Now, I can write equals to alpha Yt plus 1 minus alpha I will keep as it is now Yt hat I will distribute Yt minus 1 actual weighted combination of the previous period 1 minus alpha Yt minus 1 hat I can write like this right. So, this is what this is nothing, but I have replaced this Yt hat with the previous period combination just I have gone back to the data and I am replacing them. So, Yt hat is a combination of say Y6 is a representative or you know outcome of Y5 actual and Y5 forecast. So, weighted combination of Y5 data previous data and forecast is nothing, but the Y6 same I have written it look at here it is nothing, but alpha Yt plus alpha into 1 minus alpha Yt minus 1 plus 1 minus alpha square Yt minus 1 hat. So, this part are nothing, but if you see this part are nothing, but this actually this term these two first two term of our series. So, we got the first two term of our series the rest how I will get I will show you now only this part I will show you the calculation. So, let us bring the pen and you see here this part now what I will do 1 minus alpha square which as it is now this Yt minus hat I will distribute I will take the combination of Yt minus 2 actual and forecast. So, what will be the formula then alpha into Yt minus 2 actual plus 1 minus alpha Yt minus 2 hat right I can write like this. So, this Y2 t minus 1 hat forecast I have replaced with the previous data Y2 minus 2 actual and Yt minus 2 forecast. So, that weighted combination I have again taken now if I distribute this part again this part if I multiply it will come like this part this part will be as it is as it is. Now, this part if you see it is nothing, but alpha into 1 minus alpha square and Yt minus 2 plus 1 minus alpha 3 is a cube into Yt minus 2 forecast. So, what we found actually this part now if you look at let me open the pen highlight point now if you look at this part this part are nothing, but this terminology. So, we got the third term also arsenic and now if you replace this Yt minus 2 hat with Yt minus 2 3 combination data combinations you will get this term and dot this is what you know the technical illustration of exponential smoothing. So, theoretically this model is the exponential smoothing formula or this or that anyone you can select either of the three. So, what I will do I will select this one this one I will take this formula I will take and carry forward to the excel because this formula is easy to understand what is this formula it is just weighted combination of previous period actual and the forecast. Once you select the weight you can get that formula and you can get the forecast and you can drag it you will get the forecast using exponential smoothing, but theoretically you are actually counting all the previous period wherever you are whether it is the 10th period first say third period or say even 30th period you are actually taking all the previous period of that preceding data and you are dragging the formula that is it the exponential smoothing model. Let us see one illustration to get a better clarity. So, here you see this is the formula expanded formula of exponential smoothing time series data a time series model. Now, suppose if you take a alpha say 0.8. So, if you give 0.8 to the immediate period that means, you are giving higher voltage to the immediate 80 percent voltage to the immediate period remaining 20 percent you have to split to the older data all the older data whatever at what at which stage you are that there of iteration that is not a matter, but initially you have to give 80 percent voltage to the immediate data. Suppose you have finalized it suppose there is a trend in the data and you could see that you want to give or say stock price. So, you want to give more weightage to the immediate period right every day it is raining. So, in last day if you have if you had a rain so, you can expect that tomorrow also today also there will be rain. So, this way you can give more weightage to the immediate period say. So, suppose 80 percent voltage you have given to the immediate period. So, then how will be the weight for the next period? The next period what will be 0.8 into 1 minus 0.8 nothing, but 0.8 into 0.2. So, it is coming out to be almost 16 percent. So, 16 percent weightage you will give to the immediate period second period. Now, first two period are counting almost 96 percent weightages. So, what will be the weightage for the third period? It will be 0.8 into 0.2 into 0.2 right. So, it is coming out to be almost 0.3 percent 0.032. So, 3 percent weightage. So, this way you can distribute to the weightages actually you are going back to the older data and your for older data you the weightage will be reduced further and it is reducing in an exponential manner. So, that is what the exponential smoothing model and also imagine that since you have given 80 percent weightage to the immediate period your first three points first three weightages are counting almost 99 percent almost. So, 96 plus 3 is almost 99.2 percent imagine this. So, this is what you know if you give higher voltage to the immediate period you can see the percentage of distribution of your weight to the immediate data immediate pass data. Now, in case you give 20 percent weightage to the immediate period. So, alpha equals to now 0.2 what does it mean? It means that you are not relying too much on immediate data you are thinking that your old data has also good merit and you want to distribute the weightage to the older data also. So, you are relying on older data also and you want to take a weighted combination of the older data, but in exponential manner it will reduce 20 percent will be the higher voltage to the immediate period the maximum weightage you are giving to the immediate period, but that voltage not 80 percent only 20 percent remaining with 80 percent you are distributing to the older data. In that case how the weightage will be distributed let us see with some illustrations say. So, 20 percent if you give to the immediate period next period weightage will be 0.2 into 0.8. So, it is coming out to be 0.6 16 percent. So, first 2 period you are giving only 36 percent imagine it, but you are distributing it. Now, third period how much the weightage? Weightage will be 0.2 into 0.8 into 0.8. So, it is coming out to be 12 percent. So, effectively how much weightage you have given to the first 3 period 20 percent to the immediate period 16 percent to the next period 12 percent to the third period. So, how much the tentative weights total sum first 3 periods. So, 20 36 plus 48. So, 48 percent weightage you have given to the first 3 period. Rest 52 percent you are giving to the older period. Now, compare the two cases 0.8 to the immediate period 80 percent weightage to the immediate period and 20 percent weightage to the immediate period what is the difference? If you give 80 percent weightage to the immediate period you are suppose data has a trend or you are thinking that you should give higher importance to the too much importance to the immediate data. Your example or say practical case of the context are like that suppose you know you have to give too much weightage to the immediate case. So, if you give 20 80 percent weightage to the immediate data you see first 3 period are accounting almost 99 percent remaining maybe you have 100 data say you are in the middle of say you are at 100 10th position. So, 109 data are there almost except 3 first 3 points in case you have you are calculating 110th. So, 106 data of older data are getting only 1 percent weightages imagine it, but first 3 period you are giving almost 99 percent weightages. But for the same problem suppose if you want to give 20 percent to the immediate period you are giving only 48 percent weightage to the immediate 3 period, but remaining 52 percent weightage you are distributing to the remaining older 106 data. So, this is what the weight selection. So, therefore, the formula we understood the calculation process you understood we may not require to follow this formula we can directly use as I mentioned say y t plus 1 hat equals to alpha into y t actual plus 1 minus alpha into y t forecast. So, this formula we can use in excel because both are same in the previous sheet I have told I have discussed that both are same look at this formula this formula and the extended formula all are same anyone you can use this is nothing, but a representative of them actually. So, anyone of them you can follow, but because it is a inclusively included the older data. So, we will follow in excel the last one the circle one that I have mentioned here. So, let us go to the illustration now the question here is that the selection of alpha is very crucial. So, initially I have assumed point 8 in the next illustration I have assumed point 2 now. Now, you might have a question that sir which alpha is best suppose there are so many participants in the course and suppose and everybody will illustrate this problem with the same data suppose if I provide you the same data on data sets of 100 data points or whatever and if I ask you to use exponential smoothing. So, which alpha to start with to the immediate period it is true that will give higher to the immediate period, but the distribution will be crucial. So, in that case how we will finalize the best alpha will it vary from person to person or it will be the same interestingly we will optimize the value of alpha initially you can start with point 8 you can start with point 2 whatever initial value we can give to the immediate period and the forecast you may get that forecast is not the best what you have to do you have to calculate the error of the model that I discussed in the you know in the measure of accuracy session. So, there whatever RMSE or MSC or in the percentage absolute percentage error whatever MAD whatever you take you calculate that error if your error is less or minimum and measure of accuracy is high in that case the corresponding alpha you have to select that means you have to optimize the value of alpha. How to optimize the value of alpha and how to finalize the best alpha for everybody that means all the participants for a single data sets will come up with the same alpha unique alpha there will be no variation in the alpha for a given data sets everybody will come up with the unique alpha we call it is a optimum alpha. So, how to optimize the value of alpha by giving some initial value that we will discuss in the example. So, let us see one illustrative example now. Suppose here initially we have taken alpha point 2 with the same data set that we have illustrated for name method as well as different type of moving average techniques. So, same data sets I have taken and initially suppose I can take a first couple of data average to start with the first forecast say period 2 or the initial period forecast to start my model. So, there suppose I have taken the first period as the forecast for the second period you can take the first couple of period average also you can take average of you know first couple of period and that you can put as the initial value forecast for the 2 or 5 whatever the period you want to start with the exponential smithing model. So, suppose this is the forecast for the second period. So, now you have the actual data of second period look at actual data of second period and forecast data of second period. Now you use the formula what is the formula that I talked about y t forecast say plus 1 equals to alpha into y t actual plus 1 minus alpha into y t forecast. So, for 2 second period suppose for third period what will be the forecast alpha say 0.2 into what is the second period actual 24 24 plus 1 minus 0.2 say 0.8 into what is the second period forecast you have already assumed it by considering the previous period adjectives or the average of couple of first period to start with. So, here it is coming 23. So, this is coming up to be say it is coming to be 23. say 20. So, this is the forecast for the third period look at see the forecast for third period exponential smithing you understood now this is what the model of exponential smithing. Then you drag this you freeze your alpha value and you drag the formula you will get the forecast for the forth coming period. For example, suppose you want to predict the 18th period forecast how will get it I will illustrate in excel, but here you quickly you can get to know. So, y 18 forecast will be alpha say 0.2 into 17th period actual what is the 17th period actual 25 25 plus 0.8 the weighted combination of the 17th period forecast how much you got by dragging the formula you got 26.43. So, it is coming up to be 26.14. Then you got the forecast of 18th period which actually company want or your data sets required. So, you got the forecast, but that is not best because this is the calculation I have explained. But this forecast you found for which alpha that you have given for any iteration you have given to the immediate period the weightage is 20 percent. The remaining 80 percent you are distributing to the older or you can say the weighted combination of actual and forecast. But this alpha is not the best we have to finalize the best alpha and look at if you calculate the absolute error mean MAD. So, here the error the gap the deviation y y t minus y t hat if you take this error we have calculated all the error here like the in the previous sessions I have discussed detail about it. And then square of like absolute value and the average is coming out to be I think we have some 16 data sets. So, MAD is coming up to 2.26 MAP percentage absolute we are coming to we are getting 8 percent almost and MSE we are getting 10. Remember for that data in exponential smoothing you found suppose 6 point something right or 9 point something MSE percentage absolute error was around mean absolute percentage error around 6 percent and here it is 8 percent. So, we can say that moving average model was better for this data actually, but it is not that you know we have not optimized this right it is for 0.2 once you will optimize the value of smoothing constant or alpha probably you may get the better error or by measure of accuracy through the exponential smoothing model we will conclude that later we will do the comparison analysis also. And MSE will be the square root of MSE so, we are getting 3.16 for alpha 0.2. Now, if we extend alpha 0.2 to 0.8 with the illustration that I have talked about look at the I will come to that, but look at here the 0.2 explanation in the graph. So, suppose you are making forecasts say on this period you are taking only the previous period and the corresponding way to the initial assumption say same as it is and then the for this period forecast you have taken the previous period actual and the weighted combination of forecast. So, these 2 data you have taken and you have the actual and forecast and you got the forecast for the third period. And then for fourth period you are taking actually now for fourth period what you are doing you are actually for fourth period forecast you are taking alpha percentage of actual alpha percentage of actual plus 1 minus alpha of this forecast value. And you are getting that and you drag it you will get the forecast through exponential smoothing model to surface anyway it is quite good it is very popular in MSE also. Now, I was talking about 0.8 so, for 0.2 illustration I have shown you the table and also the graph, but for 0.8 I will show you in excel, but if you see the final graph for both the cases look at here. So, 0.8 which says a green color look at 0.8 is a green color and 0.2 is the red one red one say look at the differences 0.8 to the immediate period means what you are giving higher voltage to the immediate period look at the trend of the green line it is it is following similar pattern of the graph look at the black one the actual one and it is 0.8 is also following similar pattern because 80% voltage you have given to the immediate period. So, it is following the similar pattern, but when you give 0.2 look at the it is averaging out with the older data because you are giving importance to the immediate data. In every case whether it is 0.8 or 0.2 you are reducing the voltage in exponential manner the voltage are been decreasing in your exponential manner, but since you are giving higher voltage to the immediate period look at the changes in the graph. So, it is depending on the problem and the statement and the context you have to finalize alpha do not worry you do not have to finalize alpha you just start with any alpha you go to the excel and optimization solver or any python code you will get the best alpha or optimum alpha for the data series. Let us go to the excel now and then illustrate this whatever we have done today for explanation smoothing model with a numerical examples ok. So, I believe you can see the excel sheet. So, here if you see the excel data same data sets I have taken same data sets I have taken and I will make the forecast for 18 period, but initial period I will start from the second period I have assumed that the forecast for the second period is nothing but the same as first period. I told you you can take the average you can take the average of first couple of period also you can take the average of first couple of period and that you can bring here otherwise same data you can take also which I have done here. So, now this is a forecast for the second period and now for third period onwards you will your actual calculation will start. So, how we will get this third period forecast look at alpha 0.2 I have taken 0.2 into second period actual 24 plus 0.8 into 23 which is a forecast for second period using the formula as they look at in the right hand side I have mentioned the color formula. So, this weighted combination I have taken and I found this forecast. For example, for Ilya station suppose we are at suppose we are at 11 period right and I will show you how we calculated the forecast for the 11 period suppose suppose we are at 11 period. So, I will show you the calculation suppose here also here forecast for the 11 period what is the alpha 0.2 into what is the forecast for 10th period t look at t you are at yt plus on 11th period. So, 10th period actual plus 1 minus alpha 1 minus alpha 1 minus alpha into the 10th period forecast using the exponential smoothing you already got it you set take that forecast and you enter it you got the forecast for actually 11th period you found the forecast of 11th period which is nothing but 28.26.82. So, this way you drag it you will get the formula you drag this formula you will get the forecast for all the all the forthcoming period and for 18th period forecast you found 26.14 whatever the forecast you found that is not a matter you calculate the RMSE or the error part because measure of accuracy is the crucial part of your model. So, here if you see the error I have taken and absolute value we have calculated and MAD I have calculated as average of them we have discussed detail I am not repeating that similarly percentage error absolute error by actual data relative value you can calculate multiplied by 100 you can you can get the MAP and the average of MAP is coming out to be 8 percent here and if you go to the square error mean square error here we are getting almost average value almost 10 right and RMSE is 3.16 now this is forecast you found for alpha 0.2 if you change it to 0.8 if you change it to 0.8 how much you are getting your MSE has come down look at 9.80 and RMSE is 3.13 whatever the forecast you are getting said earlier it was 26. something now 25.55 that is not a matter matter is that how much your RMSE or error part MSE part or percentage error part. So, for 0.5 you are getting different forecast and the RMSE different and MSE also different. So, which alpha is best for this particular data sets which is been kept in column number D. So, let us see so the corresponding forecast of to a period 18 may get finally. So, let us go to the data and go to the solver how to install solver and how to run it how to put the data import the data into solver I have discussed in the previous session. So, I am not going to repeat that just see how we are getting the optimum value. So, we have selected RMSE as our objective function and it is a minimization problem. So, we will select the minimum cell and then the decision variables are alpha we have to optimize that alpha value. So, we will select this particular cell and then the conditions will add the alpha should be 0 to 1 right. So, I have put that look at the conditions alpha 0 to 1 how to add this you can go to change or add you can do it alpha should be less than greater than whatever integer binary whatever you want to put here it is less than 1 and alpha should be greater than 1 you can click here also variables cannot be negative. So, you can click this non negativity conditions and it is a non-linear problem it is not a linear simplex algorithm it is a it is not a linear problem because MSE and RMSE are a non-linear form. So, you have to select non-linear gradient method of non-linear process which is been developed by Microsoft do not select the simplex LP you have to select the non-linear problem because it is a RMSE is a non-linear. So, solve it look at the optimum alpha we found how much 45 percent to the immediate period for this data set wherever in your iteration 11th period, 3rd period, 18th period your immediate period of weightage you are giving 45 percent rest you know 55 percent weightage you are distributing to the older data and this is the exponential smoothing formula of time series analysis. And you got the best RMSE and the corresponding forecast here look at you cannot get lower than this RMSE or MSE value you put with any alpha let us put 0.8 you are getting 3.13 which is higher than the optimum RMSE you put suppose if you put 0.8 and if you go to data again if you solve it will come up with the best alpha, solver will search all options of alpha between 0 to 1 and they will come up with the best alpha and they are giving the optimum output actually and the corresponding forecast this is what the exponential smoothing model. Remember in the beginning of exponential smoothing concept I talked about the you have to optimize alpha initially all the participants can start with any alpha look at any alpha you can start with any alpha 0.2 you put 0.2 not a matter you can go up go to data and you optimize solver will find the best optimum value of alpha and the corresponding RMSE. So, everywhere you are getting the best optimum value and all the participants if you practice with any problem with this excel illustration with the formula iterative process or in python also you will get the best alpha or optimum alpha or unique alpha for everybody for the same series of data. If you change the data sets your alpha will change definitely because pattern the behavior of the data will change. So, corresponding alpha will be the different, but you have to optimize it initially you can start with anyone, but the optimum alpha you have to finalize through this optimum process of iteration. So, this is what the exponential smoothing model. Now, let us come back to the PPT then I will discuss one interesting concept now that we understood the exponential smoothing model right and the optimum alpha for a given data set how to select the optimum alpha that also illustrated using excel of the data we finalized it. Now, let us see one drawback of the exponential smoothing model that if the data has a high uptrend or downtrend pattern that means suppose data has a uptrend pattern or say downtrend pattern. Suppose you have a uptrend pattern of data suppose in that case this exponential smoothing formula give if you find alpha say 0.2 or say 0.5 say if you select alpha in that case what happens it will smooth out the data and the forecast might be like this. If you put higher alpha say 0.8 it might forecast like this to some extent, but it may not come like this it will not go in the trend of the data it may not capture the trend of the data effectively. So, therefore exponential smoothing has a drawback or limitation if the data has a strong uptrend or downtrend to some extent steady data stationary data if you have this model is very good I have shown you the illustration, but look at this sample example suppose you have a data say sales of a product month wise in a decreasing manner. So, in January it is 1325, but in May it is 1210 there is a strong decrease in February it is a high, but overall if you see the pattern of the data look at that this black cell data black graph data the actual data it is a downtrend data. So, if there is a solid downtrend can we use the exponential smoothing model that we discussed today look at moving average models will also not fit for this particular data sets we have discussed that also which model is most suitable for that data we will discuss in the next session, but today let us understand the drawback of exponential smoothing model. So, can we use exponential smoothing for this model the answer is no why look at that we have selected alpha 0.2 that means, immediate period for the month of May for the month of May we have given 20 percent weightages remaining 80 percent we have smoothed out. So, here if you see the data the forecast is coming using exponential smoothing I will show you in excel the forecast is 1309 is it a good forecast look at there is a downtrend in the data and your May actually 1210 your June should be lower than 1200 right. So, it could be say 1200 or 11 something something, but you are getting 1309 with this exponential smoothing model of 20 percent to the May data remaining 80 percent you are giving to the older data. So, therefore, you are giving importance to the February March data also. Therefore, this model is coming up with ending up with the forecast of 1309, but look at the graph 1309, but you will find a big error right big error the RMSE will be quite high. Now, if you increase alpha 0.8 the way we have discussed in the previous examples if you select alpha 0.8 look at 80 percent weightage you are giving to the month of May 80 percent weightage you are giving to the month of May data. So, in that case what happens your forecast is to some extent better than 0.2 how much 1225. So, that means, higher alpha is better if you have a trend up up trend or downtrend data look at here for 0.8 for 0.8 your forecast is this to some extent you know may be your actual will be like this say to some extent 5 better with 0.8 the error is less less error you are getting right. So, therefore, which alpha is the best 0.2 or 0.8 let us go to excel and illustrate this particular example and let us see what alpha the optimum solver gives to us go to excel again and I have written the data here and if you see enter data I have kept here and I will make a forecast using this exponential smoothing model initially I have kept 0.2 right same formula as it is RMSE I have calculated I will go to data for your to save the time I have done enter calculation and I will show you the solution only go to solver same like alpha range optimum value enter encoding of the data I have done non-linear optimization as it is I will solve it look at RMSE is 43 and alpha is 1. So, look at the forecast it is ending up with the same method like name method kind of thing same data it is forecasted it has not smoothed out with the older data experiences smoothing each failed here actually it is not taking the weighted combination in exponential manner with the welder data it is ending up with the just immediate period 100 percent weightage they have given to the immediate period. So, this is the drawback of the model if you have up train or down train data. So, let us see with 0.8 also if you start with 0.8 and if you solve it again look at here again it is ending up with alpha 1 since alpha cannot be 1.2 say alpha range is say if you put 120 percent you might get a better forecast, but you cannot increase alpha more than 1 right. So, range is 0 to 1. So, it is ending up with alpha 1 and it is ending providing like a name method forecast kind of thing no exponential smoothing is been done no weighted average are been taken into account just fast period is been taken into consider as a forecast for the succeeding period and this is for the drawback of the exponential smoothing models. So, then how to overcome it because if there is a up train or down train data it is saying that you know exponential smoothing cannot make better forecast because there is a limitations you cannot increase alpha more than 1 and it is ending up with alpha 1. So, probably here with alpha 1 you can see 12.10, but perhaps I will show you tomorrow the hold model which is extension of this concept you will get the forecast will be like 11 say 65 or maybe 1175 something. So, this type of forecast will come with the data pattern actually how we will get this new forecast actual value we will get to know once we will open the actual forecast value using hold model, but just tentative I am talking about it will be below actually 2100 may be 1190 or 1180 kind of thing will come as a forecast. How come you will get an what will be the corresponding alpha and the corresponding trained part you have to consider and you have to taken into account how to do that that we will discuss in the next session through hold model. So, let us come back to the you know PPT now. So, today let me go back to the summary sheet. Today we have discussed only the concept of exponential smoothing model simple exponential smoothing model how it works, what is the features of it, how it is been derived and how it can be calculated and the corresponding smoothing constant can be optimized. That we have found we understood next class what we will do we will extend the exponential smoothing constant concept to hold model when there is a uptrend or downtrend data. So, let us conclude today's session with these discussions.