 then we will come to the smoothing technique. And why the smoothing technique is required, because series do not show continuous trend, there may be seasonal and the random variation. As we discussed, there may be the secular trend, there may be the seasonal trend, there may be the cyclical trend, there may be the random variation. So, series that do not show continuous trend, either there is seasonal or there is may be random variation. And generally the smoothing technique is used to smoothen this variation and then forecasting the future value. Since there is a variation, the smoothing technique is being used to smoothen the series and then on that basis, the future value can be forecasted. Then we will see what are the smoothing techniques. So, because smoothing is generally used to smooth the variation in the variation in the series or the variation in the time series data, so that there will be more accuracy in the future forecasted demand or there is more clarity in the future forecasted demand. So, there are three methods of smoothing technique. The first one is moving average and in the moving average method, the forecast on the basis of the demand value during the recent past. So, here if it is D is the demand is the time period n. In this case, we take the d i that is some total of the d i divided by the number of the observation. So, in this case moving average the forecast is on the basis of the demand value during the recent past. And here the if you look at this i stand takes from value from 1 to n and here it is the most simplest version of the smoothing technique, but here we take because here we take the basis of the demand value only from the recent past. Then the second technique is weighted moving average. It is the forecast on the basis of the weights of the recent observation. So, here if you look at the demand is on the basis also, not only the demand in the previous time period also the whatever the weight access to this demand in the previous time period or whatever the weights for the specific variable that also taken into consideration in case of the weighted moving average. So, weighted moving average is not only the not dependent only on the past demand rather also that what is whatever the weight assigned to them those variables that is also taken care in case of the weighted moving average. Then the third method is exponential smoothing and in case of exponential smoothing generally it assigns a greater weight to most recent data as to have a realistic estimate of the fluctuation. So, this is again more improvement more revised form of the whatever the weighted smoothing technique and in this case generally it assigns this technique generally assign a greater weight to most recent data as to have the realistic estimate of the fluctuation. Rather if it is a time series data of 10 years more importance given to the past year past 2 years past 1 year rather than the similar weight to the across the year from all this 10 years in this case the weight is given more to the specific year which is just before this present period. So, here the weight vary between 0 to 1 if it is 10 years and if the forecaster they feel that 10 years data is not going to be that much relevant may be they can assign 0 weight to the 10 year data and may be the again the numbering start from 9 the may be the less weight to the 9 again may be little bit more to the 8 and similarly if it is for time period 1 the time period 1 it is more assignment will be given or more weight will be assigned to year 2. So, here if it is the forecast in the for the next time period that is t plus 1. So, the functional form takes it is equal to a plus d t plus 1 minus a f t. So, here if you look at the demand is more dependent on that whatever the forecast value of this present time period because here we are forecasting the for the next time period and what is past period for next next time period this present time. So, if you are doing it for the t plus 1 time period more weight will be assigned to time period t rather than any other time period because the past year the way measure weight or the more weight is given to the past year data. So, f t plus 1 is 0.30. So, if you take the example f t plus 1 is 0.30 and here it is we are considering 0.70 as the forecaster demand for the present time period. So, here if you look at this forecast demand for t plus 1 may more come from because 0.7. So, 70 percent come from the forecasted demand for this present time period and 0.3 for the demand for the rest of the time period. So, if it is f t plus 1 is equal to 0.30 d t plus 0.70 f t in this case for future forecast for forecasting of demand for the next time period the present time period is t for the next time period if the future forecasting is for t plus 1 period 70 percent weightage will be given for the forecasted demand for the time period t and rest 30 percent will be given to the demand for the time rest of the time period. Then we will talk about the second methods under quantity method that is barometric technique and what is barometric technique? Barometric technique is the to define it the prediction of the turning points in one economic time series through the use of observation on another time series called generally the barometer of the indicators. And generally barometer is one who generally records all these activity or generally maybe crystallize all this fluctuation in the economic activity. So, in the barometric technique generally a index is constructed on relevant economic indicators and forecast future trends on the basis of this indicator. So, what how this barometric technique is being practiced? Index will be constructed and what will be the component of the index? The component of the index will be the relevant economic indicators and once the index will be constructed on that basis future trend will be forecasted on the basis of these indicators. Now, what are the indicators in this case taken for the construction of the index? We take three types of indicators. One is leading indicators, second one is the coincident indicators and third one is the lagging indicators. What is a leading indicators? Leading indicators is one where the series that goes up or down ahead of the other series. So, if the one series is about price quantity, another is about the income quantity. In this case if the price quantity series is always going up the income and quantity series, we can say that the price quantity they are the leading indicators as compared to the income and quantity. So, leading indicator is one and where the series always go up or down ahead of the other series. Then we have the coincidence indicator and what are the coincidence indicator? This is typically a series that moves up or down simultaneously with level of economic activity. Whatever the series simultaneously it move and move up and down. So, in a specific time period moves in a specific time period it comes down. So, moving up and coming down there is there follow a regular trend and that is why this is called as the coincidence indicator because the series it moves up with the increase in the economic activity down with the decrease in the economic activity. Then the third type of indicators is lagging indicators and lagging indicator is series which moves with economic series after a time lag. So, if the economic is economic economy is going through the boom in period t, this indicator will move in the t plus 1 period. It will not move in the t period because it is a lagging indicator. If economic activity is more in time period t, this indicator will be moving up in time period t plus 1 and that is why this lagging indicator is known as the series which move with economic series after a lag of the time period. Then the so first we had the trend projection method, then we have the barometric methods in the quantitative method. Then the third method is econometrics method and what is econometric method? Here we take two kind of analysis. One is the regression analysis and second is the simultaneous equation methods. So, regression analysis generally relates the dependent variable to one or more independent variable in the form of linear equation as we discussed when we were discussing about the regression analysis. So, correlation essentially talks about the relationship between two variables whether they are positively related, whether they are negatively related and regressions talks about that what is the extent of the relations or in which direction or what is the magnitude of the change in one variable when the other variable changes how they are related that we generally do in the regression analysis. So, generally regression analysis relates the dependent variable into the independent variable in the form of a linear equation and this is instruments to the casual forecasting. Now, we will see how this regression analysis generally useful in the forecasting method. So, before that we will see that there are three type of regression analysis. One is simple or bivariate regression analysis where it is basically the relationship between two variable one dependent one independent variable they are linearly related. Then this in case of two variable regression also if they are not they are not related line linear rather they are related in a non-linear way we get a non-linear regression analysis. And when we study the relationship between one dependent variable and the number of independent variable we get the multiple regression analysis. So, simple regression analysis is the relationship between one dependent and one independent variable non-linear relationship when the variables are related in a non-linear way and multiple regression analysis where the one dependent variable which dependent on the number of independent variable and this kind of when the functional form or this kind of equation that is generally the multiple regression analysis. Next we will see how this regression is used for forecasting methods. So, if you are taking a simple analysis of simple regression analysis example of simple regression analysis suppose d is equal to a plus b p and here we say that both the variable they are linearly related there is a linear relation between d and p. So, d is the dependent variable p is the independent variable. Now if you plot it we have different series of the value for d and p and we will get the combination here and if you plot it in the graph maybe we will get a combination one combination is p another combination is q another combination is r and another combination is s. So, what when p takes a value what is the value of the d when p takes a different value what is the value of the d on that basis we get all this point. So, this point talks about that how both of them they are related. Now here is if you look at this is the regression line and if there if this is the if the combination between this d and p is in this line we feel that they are the best fit because they are lying on the regression line. But there may be some random variation and if you incorporate such variable why why there is a random variation because here if you look at q and r they are lying on the regression line whereas p is lying above the regression line and s is lying below the regression line q and r is the in the line. So, when we consider that there is a random variation if there is a random variation now how this regression equation will be this will be a plus b p plus e because e is the random term related with the variation in the related with the random variation. So, now to minimize this random term we need to calculate the deviation from mean or we need to calculate what is the distance of all this point from the regression line. So, for that we need to find the value of a and b and how this value of a and b will be used this value of a and b will be used to minimize the square deviation of square deviation between the line and the actual data point. Because basically here we are trying to here we are trying to manage that whatever the deviation in the regression line and the on the points on the actual point that we need to that we need to generally minimize and to minimize this we need to find the find the value of a and b and through the value of a and b we can minimize the square deviation the sum of square deviation between the line and the actual data point. So, once we know that this value of a and b that is going to give us or that will helps to minimize the difference between the actual data point and the actual data point and the regression line then we get the estimates of a and b in that point. So, once we get the estimates of a and b suppose this is as a k 1 b k the new regression line will be a k plus b k p and here we say that this value of a and b takes care of the deviation from the regression line and the actual point. Here we get a time that term that is explained sum of square this is the measure of predictive accuracy of regression equation. So, if it is smaller E s s if the value of this is small then more accurate and if it is closer the line then this is the best fit because the deviation between actual point and the regression line is actual point and the regression line is minimal. So, now we find out the coefficient of determination to find out how these two variables they are related. So, to find this we need to find out the total sum of square total sum of square is the explained sum of square plus residual sum of square and so R square is explained sum of square and total sum of square or we can just reprimand this as T s s minus R s s divided by T s s. So, this is 1 minus R s s by T s s and if R square is R square has to be non-negative because it talks about the coefficient of the determination like what is the explanatory power of this model altogether then and this should be always 0 R square less than equal to 1 and if R square is equal to 1 we call it a perfect fit. Now, how this regression equation can be used for forecasting the demand. So, till the time what we have seen in the regression equation that we are trying to minimize the error. So, once we get the best fit regression line on that basis we can forecast these are the actual data point which is also best fit because there is a accuracy in the projected and the plotted and once we get that regression line best fit regression line on that basis now we can forecast the future demand. Then what is the what are the problems in this econometrics method specifically in case of the regression analysis. We can find the value of a and b on that basis we can forecast the demand and also to minimize the error we can also find out the value of a cap and b cap because that also takes care of the minimization of the error between the regression line and the actual data point we can forecast the demand. But what are the problems or what are the challenges being faced when we use the regression method to forecast the demand. The first problem is multicollinearity here two or more explanatory variable in the regression model are highly correlated that is why you call it say multicollinearity problem and since they are highly correlated the impact of each individual individual independent variable on the dependent variable becomes difficult to ascertain. So, they are correlated so what is the impact of the independent variable individual independent variable on the dependent variable finding that is difficult. So, like consumption of an individual is affected by the income and wealth of the individual and if you look at income and wealth they are they are closely related. So, in this case the detection of removal of multicollinearity is important because otherwise difficult to find out what is the contribution to consumption from the income and what is the contribution to consumption on the wealth of the individual. So, this multicollinearity can be removed by inclusion of omission of variables additional data increase sample size and the intervention of the advanced statistical tool. The second point is autocorrelation and when we get this condition of this autocorrelation this is the condition where error terms e in the regression equation are found to be serially correlated or also called as the serially correlated rather than autocorrelation. It can occur both in time series as well as cross sectional data and to correct this autocorrelation problem generally we use the Durbin Watson test to see that the error terms there at least not serially correlated. Then the third problem is heteroscedasticity and what is the problem of heteroscedasticity because the regression model always assumes that the variance of error term is constant for all values of the independent variable in the model. But if the variable have different variance then we generally land it to the heteroscedasticity situation and this disturbance leads to biased estimator of the true variance and there is no particular rule for detection for heteroscedasticity mostly it is detected by the experience and it can also can be overcome by running a weighted least square regression like giving a weight to each of this variable or may be through the smoothing technique this weighted average mean or the weighted least square can be used to solve this problem of heteroscedasticity. Then we have a specification error it occurs when one or more independent variable in the regression model is omitted when the structural form is wrongly constructed. So, we take the example like in a demand forecasting regression of consumer omitting income of consumer leads to specification error and example 2 is the demand function is non-linear, but if it is estimate to linear it leads to the specification error. Then identification problem typically this typical example taken in case of identification problem is if it is required to determine the effect of quantity demanded of a good when the price is increased by say 10 percent historical data of monthly demand and price will not give the solution as price is the part of the multi equation system. So, supply of the good also need to be taken in the account to avoid the biased parameter. So, there is also the problem of identification in case of the regression. So, the second method or the second method of the this econometrics is come as the simultaneous equation method what is generally used to forecast the demand. Now, what is the simultaneous equation method based on the guiding principle that any economic decision every variable influence every other variable. So, any economic decision all the variable influence the every other variable like you take the example of decision on optimal advertisement expenditure depends on expected sales volume volume of sales is influence also by the advertisement. Example to quantity demanded of the T depends on the price of coffee and also price of coffee get influence by the quantity demanded for the T. So, if you look at the variable they are related to each other and that is why all the variables they influence the other variable every other variable when it comes to economic decision. So, since there is a simultaneous and two way relationship between this two way this between the variables which influence for or which requires to forecast the demand it is not possible to capture such relationship using the single equation models like a typical regression model. Hence, the need of simultaneous equation method comes here and a typical simultaneous method comprise of endogenous, exogenous structural equation and definitional equation. What is endogenous variable? Endogenous variable are those which system seeks to predict are included in the model as the dependent variable and number of equation in the model must equal to the number of endogenous variable. Exogenous those are given outside the model and it is not a if you look at the number of equation is not dependent on the exogenous variable. Then we have structural equations structural equation are those equation which seeks to explain the relation between the particular endogenous variable and other variable in the system and definitional equation are those equation which specify the relationship that are considered to be true by definition. So, through this four components generally the simultaneous equation method is used. So, the detailed description of this method is not within the scope of this typical course of this typical session. So, that is why we have just identified this model that how this model is being used to forecast the demand. Now, what are the limitation for this demand forecasting? Because in the previous class we talk about the subjective methods of the demand forecasting and in this class we talked about the quantitative method of demand forecasting and as a whole there are few limitation of the demand forecasting and what are those limitation we will just check that. Past data and events are not always the true predictors of future, because the whatever the events that may not recur in the future time period and also about the trend that may not also occur. Because as a whole if you look at the time period is dynamic whatever the previous time period the next time period may not happen in the same way. Then if there is a change in the fashion again forecasting is difficult because if you are doing a forecasting for this in the for next 5 years may be the fashion has changed people they may not going to buy the same product and that is why it is difficult to do the forecasting for the product. Consumer psychology changes with the time. So, again this there is a difficulty in capturing the consumer psychology and on that basis doing the demand forecasting it is costly because it is a existing process to do this forecasting and when there is a if you look at there is lack of forecasting experts and also there is a lack of past data for forecasting which creates another challenge for the demand forecasting typically for the economic organization. So, whatever we discussed in the previous class on demand forecasting and in today's session about the demand forecasting to summarize this we can say that forecasting is an operation resource technique for planning and decision making it is a scientific analytical estimation of demand for product service for a specified period of time and this is categorized on the basis of the level of forecasting on the basis of the time period on the basis of the nature of goods. And we have two techniques of demand forecasting qualitative where we consider the consumer opinion survey, sales force composite, export opinion method, market simulation and test marketing and we have quantitative methods where we discuss about the trend projection, smoothing technique, barometric technique and also the econometric method. So, these are the and also we discuss about some challenges about the demand forecasting particularly when the time is dynamic the consumer psychology changes and also there is a difficulty in getting a good forecast expert or depends upon that the whatever the past data that is also non availability of that also poses a challenge for the demand forecasting. Nevertheless, demand forecasting is always helps the firms to plan their output, plan their distribution, plan their procurement of the raw materials, but still there are few challenges to face if the demand forecasting has to be done.