 So in today's session we will continue our discussion on demand forecasting. So if you remember in the previous class we talked about that what is the need for demand forecasting, what are the different techniques of demand forecasting after the different steps involved in that, then you talked about the methods of the techniques of the demand forecasting typically more on the subjective part of it. And generally that is known as the subjective or the qualitative methods of demand forecasting and in today's class we discuss about the quantitative method of demand forecasting. So to start with that why we need these quantitative methods for demand forecasting, if you look at subjective methods can be used only when past data is not available and when past data is available it is advisable that the firm should use statistical tool as it is more scientific and cost effective. So if you remember in case of when we are discussing about the subjective method we also discussed that if subjective method is generally used if it is a case of a new product getting into a new market or doing some improvement in the market or getting into a specific segment of the market. So in this case subject method is generally more valid because here there is no past data is available, but when the past data is available it is always advisable to get more scientific more accurate demand forecasting and also more cost effective demand forecasting it is better to use the statistical tools. So that on the basis of the past data you can use the statistical tools and you can get a more effective or the accurate demand forecasting. Generally this case typically in the quantitative method it is more depend upon that whatever the past data available about the quality and quantity of the past data and that gives more clarity about the accuracy of the demand forecasting. So when it comes to the quantity method of demand forecasting essentially it depends upon the time series of the past sales. So to discuss about this quantitative method of forecasting we will take first the trend methods and in trend methods the trend projection and here basically we use the time series data and what is time series data? Time series data when we keep the when we record the information on a chronological basis maybe it is on a weekly basis only monthly basis only day basis quarterly basis our basis or the yearly basis when we order this when we arrange this data on a chronological order on the basis maybe weekly monthly yearly or maybe in a hour basis or the day basis generally that is known as the time series data. And this trend projection this method typically looking at the past data whatever the trends is being there in the past data using this quantity method typically the trend projection the projection will be done on the basis of the past trend of the typical data. So here the basis for this trend projection is the time series data because time series data gives the trend because it is on a chronological order and we get the full set of data and it gives a trend that whatever the behavior of that typical variable in the past time period and after getting the past sales data the projection will be done in case of the future time period or the projection will be done what will be the demand for that product in the future time period. So in case of time series data mainly there are four components first one is secular trend and in case of secular trend generally the change occurs consistently over a over a long time it is relatively smooth in its path. So we know that in case of secular trend means it is equal if you look at it is a the trend whatever the change in the trend suppose it may happen that in the time series data if you have 5 years data the trend is that may be every year in a particular month it increases or every year in a particular month it decreases or may be in the beginning quarter it increases in the end quarter it decreases. So the demand whatever the change in the demand that remains same in case of the secular trend and this change occurs consistently over a long time it is not that it is just changes for one year the next year it is not changing or the third year it is not changing rather whatever is the change it goes on for a long period of time and that is why this is known as the secular trend and in case of secular trend the change occurs consistently over a long period of time and relatively smooth in its path and why it is smooth because it is consistent and it occurs for a long period of time. Then the second component is a seasonal trend and generally the seasonal trend is the seasonal variation in the data within a year. So, suppose this is if you look at we take a product that this is the demand for ice cream. So, what would be the seasonal variation here? So, obviously in the summer season it is going to be high in the winter and rainy season it is comparatively low and this variation will be there throughout the time series data within a year in each summer the variation is there because there is an increase and the other part is decrease. So seasonal trend is generally similarly if you take the case of the winter garment obviously the demand has to be more in case of the winter season and less in case of the summer season. So, in this case we need to see the product is what kind of product whether it is a seasonal product and if it is a seasonal product generally the variation is also in the data within a year in that specific season where the data been generally being used or the product generally being used. Then thus the third component is a cyclical trend and here there is a cyclical moment in the demand for a product that may have the tendency to recur in a few year. So, if you remember about the business cycle we discussed about a business cycle generally the economic activity follows a different path sometimes it goes to the boom sometimes it goes to the recession. Similarly, when in case of cyclical trend the trend also follows a cycle and it increases then after sometimes it decreases and the same increases get followed also in the next time period. So, whether it is a boom whether it is a recession it follows the same kind of variation in next time period or maybe after a few time period that is why this trend is cyclical because this is a cyclical moment. So, if it is increasing now it is not that the next period it has to decrease next period it has to increase or the next period again it has to increase it follows the cycle if it is increasing now maybe after few years or after few months whatever may be the basis for the data on that basis it may increase again and that is why this cyclical trend is a possibility here is that the tendency is that the same kind of change or the same kind of variation has to recur in a few year. So, cyclical moment in the demand for a product that may have the tendency to recur in the few days or few years or few months whatever may be the basis for the time series. Then the last component of the time series is the random event and what is random events? Random events is generally when the variation comes from the random events and what are the typical variations. So, if you take the case of your natural calamities your social unrest in this case there is no trend of evidence has created a random variation in this trend. Because the social unrest is happening it is not happening very frequently that there will be evidence in each year 10 times this is the demand when there is a social unrest. It is not a regular feature and if it is not a regular feature the evidence it is difficult to find in the time series data maybe it is a social unrest we put 20 years and social unrest now. So, since this time series suppose in this case we are taking a time series of data of last 5 years if there is no evidence of the social unrest in last 5 years whatever the variation in this case particularly for the social unrest that has to be random and because this is a random event. Similarly, for the natural calamities like if the flood has happened this year and if the flood has not happened in last 5 years whatever will the effect on the demand that will be of course the effect of because of the effect is on the trend due to natural calamities and it is always the random because it has not happened in the previous time period. So, when the variation occurs due to random event the variation has to be random because there is no evidence of such kind of variation in the trends. So, there are four components of price time series data one is the cyclical trend second is the random event third is the seasonal trend and fourth is the secular trend. Now, what are the component of this time series? So, this whatever the component we discuss here if you can put it in the formulate in the equation form then y that is put in the time series that has to be equal to the t plus s plus c plus r here c s is the secular trend c is the cyclical trend r is the random event and t is the seasonal trend and if you so if this can be in the edit addition form or it can be also in the multiplication form. So, the first one is that is t plus s plus c plus r is the additional form and y is equal to t s c r can be the multiplicative form and if you are taking the logarithmic transformation of this multiplicative form then we will get log y is equal to log t plus log s plus log c plus log r. So, here the entire trend has four kind of components and this can be done this can be formulate either in the additive form or in the case of the multiplicative form and multiplicative form again we can transfer into the logarithmic form. Now, what are the methods for this trend projection? So, till the time we are talking about the components of the time series data because for the trend projection the basis is time series data. Now, we will see what are the methods for the trend projection and what are the methods for the trend projection? The first one is the graphical method as the name suggests generally in this case the projection will be done in the using a graph. The past values of the variable in the different time is plotted in a graph and movement of the series s s and the future values are forecasted. So, in this case we will identify here we need to forecast the demand. So, in that case we will see what are the two variables to forecast the demand may be on the basis of the advertisement what will be the what will be the sales or on the different or may be in the previous time period in its specific time period what was the demand for the product. So, time and quantity will plot it in a graph will follow that will see the series will plot a line will see the series and after looking at the series we can forecast if this was the trend in the last 5 years what is going to be trend or what will be the forecasted demand for this product in the next 5 years. So, looking at the past trend using the graphic method generally we can forecast the future trend. So, we will just take a graphical explanation to this graphic methods and how generally this trend is the projection of the trend is done in case of the graphical method. So, here we can take time here we can take quantity suppose this is 2005, 2006, 2007, 2008, 2009 and 2010. So, here it is 0 sorry this is may be 10, this is 0, this is 20, this is 30, this is 40, this is 30, this is 50 and so on. So, suppose we have the data about last 5 years 2010 or last 6 years that is from 2005 to 2010. So, suppose in 2005 we have 2005 we have 9, this is the time and this is the time 20. So, 2005 it is 9, 2006 it is 12, 2007 this is 10, 2008 again we can say this is 20, 2009, 22, 2010 may be again we can say this is 15. So, now if you plot this for 2005 this is 9, for 2006 this is 12, for 2007 this is 10, 2008 this is 20, 2009 this is 20, 2010 may be this is 15. So, if you look at here this is the trend for the quantity this is the trend for the demand in the last 5 years. So, if you look at now from 2005 it increases again it has decreases in 2007, again it has increases in 2008, 2009 and decreases in 2010. On this basis now we need to project the future demand on the basis of this past trend. So, graphical method generally first plot it, look at that how is the series, how is the movement of the series assessed and then the future value is forecasted. So, now it has to see that why the value is less, why the demand is less in 2007 or why it is following a declining trend in 2010. So, on this basis now the series will be assessed that why in a specific year or why in a specific time period the demand is more or demand is less, whether the same thing has to be taken into consideration when we are forecasting the demand for the next 5 years also. So, in this case graphical method is simply plotting the data of the dependent and the time and the demand in the past time period and after putting it in the graph the series will be assessed and the future value will be forecasted. So, in the trend projection method the first method comes as the graphical method. Then we will take the least square method and what is a least square method. If you look at if you remember this we discussed when we are discussing about the regression this typical least square method and this is basically a tune to estimate the coefficient of a linear function based on the minimization of the square deviation between the best fitting line and the original observation given. So, if you remember when we discuss about this in case of the regression that we get the error because whatever the regression line and whatever the actual that there is a difference between these two and since there is a difference between these two this gives us the error. So, to minimize the error on the basis of the square deviation between the best fitting line and the original observation generally the method of least square is used and this method of least square also being used to project the forecasted demand. And how this demand will be forecasted on the basis of the least square? We will just see that we will find out how we can find out the value of a and b and after finding out the value of a and b on that basis we can forecast because b gives us the slope. Slope generally gives us the whatever the whatever the increase in the dependent variable when this typical variable changes and that is why on that basis we can project the demand. So, here we will take the least square method to understand this. So, here y is equal to a plus b x and from there we get the normal equation because this is the case of the minimization we get the normal equation as sigma y is equal to n a plus b x and e x y is equal to a e x plus b e x square and to solve this trend equation. So, these are the trend equation and on that basis we need to first solve the value of a and b because this is a trend equation and the basis of the value of a and b now we can find out what will be the we can find out what will be the value of the future in the future time period what will be the value of a and b. Now, what is a and b here a is the value of intercept and b is the value of the slope and the value of intercept and slope will decide what will be the demand for the product in the future time period. So, to solve this trend equation we have to solve this trend equation and for solving this we need to follow the least square method. And following this least square method we get A is equal to E y by n and B is equal to E x y by E x square. So, here y is our dependent variable x is the independent variable this is the sum of the dependent variable by the number of observation this is the sum of both x and y dependent independent variable divided by the square deviation square root of the square of this independent variable. So, once we get the value of A and B on that basis now we can project whatever the trend of the future. So, in this case in the trend projection first in the first method we generally do it through a graph we plot the dependent and independent variable or the time typically the past time period whatever the demand that we plot it in the graph. And on that basis we generally assess the series on that basis we forecast the value of the value of the demand in the next time period. In case of least square method generally we follow the least square method of solving the normal equation finding out the value of slope and intercept. And once we get the slope and intercept on the basis of the past data then we can project that project the future A and B because A is the intercept B is the slope on that basis the demand is dependent on that whatever the change in the independent variable. So, once we get A and B on that basis we can plot the we can plot or we can project the what will be the future trend or what will be the future demand for this specific product. Then the third method is Arima method and this is also known as the box and Jenkins method and how generally this Arima method is being followed to do the trend projection. In the stage one we need to underline the trend in the series removed with the first differences of the successive observation. So, whatever the underlying trend in the series that has to be removed by with the first differences we need to take the first order derivative of the successive observation. Then stage two possible combination will be created on the basis of the autoregressive term on the basis of the moving average term and the number of differences in the original series of adequate fit into the series. So, there will be possible combination will be created on the basis of the autoregressive term on the basis of the moving average because Arima method is one which also consider the autoregressive term and also the moving average term. So, in this case the possible combination will be created on the basis of the autoregressive terms and the moving average term and then the number of differences in the original series will be adequately fit into the series. Then stage three the parameter estimation will be done and the parameter estimation for doing the parameter estimation will follow the least square methods and stage four is generally to do the goodness of fit that is tested on the basis of the residual generated repeat if it is not a good fit. So, initially first we do the we will take out the underlying whatever the trend in the series. Then we will find out the combination on the basis of the moving average and on the basis of the autoregressive terms. Then we will do the parameter estimation following the least square method and stage four is generally to do the goodness of fit to find out what is the overall explanatory power of the model. And in this case if you find that this model is not going to fit if it is not fit again we have to start from the stage two where again we have to find out the combination with the reference to moving average term and also the autoregressive term. And stage five if you find this model is qualifying the goodness of fit or the level of significance is acceptable then we will use the coefficient to forecast the future demand. So, stage one is always to start with the whatever to remove the underlying trend in the series and stage three is the parameter estimation on the basis of the combination of stage two. And then stage four is goodness of fit and here we need to see that if it is miss fit generally we need to repeat stage two again. And finally, stage five whatever the coefficient we get on that basis we can forecast the future demand. So, trend projection methods under quantitative method trend projection method is one where we generally use the graphical method or the least square method or the ARIMA methods to project the future trend or project the future demand. 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 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. And 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 assess 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 assign 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 maybe 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 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 major 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 forecaster 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 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 rest of the time period. Then we will talk about the second methods under quantitative 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 indicator. 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, 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 are 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 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 related 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 may be 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 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 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 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 points that we need to that we need to generally minimize and to minimize this we need to 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 ESS 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 re frame it this as TSS minus RSS divided by TSS. So, this is 1 minus RSS by TSS 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 all together 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 is a 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 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 they are at least not serially correlated. Then the third problem is heteroscedasticity and what is the problem of heteroscedasticity because the regression model always assume 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 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 this econometrics is come as the simultaneous equation method what is generally used to forecast the demand. Now what is this 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 if you take the example of decision on optimal advertisement expenditure depends on expected sales volume volume of sales is influenced also by the advertisement. 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. So the 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 difficult 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 quantity 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 exhaustive process to do this forecasting. And when there is a if you look at there is a 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 products 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 considered on the basis of the nature of goods. And we have two techniques of demand forecasting qualitative where we consider the consumer opinion service, 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 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 availability of that also possess a challenge for the demand forecasting. Nevertheless demand forecasting is always a 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.