 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 stool 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, subjective 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. And generally this case typically in the quantitative method, it is more dependent 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, may be it is only weekly basis, only monthly basis, only day basis, quarterly basis, hour basis or the yearly basis, when we arrange this data on a chronological order on the basis, may be weekly, monthly, yearly or may be 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 this 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 is 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 a 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 generally being used or the product generally being used. Then thus the third component is cyclical trend and here there is a cyclical movement in the demand for a product that may have the tendency to recur in a few years. 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 cyclical movement. So, if it is increasing now it is not that next period it has to decrease next period it has to increase or the next period again it has to increase it follows a cycle if it is increasing now may be 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 years. So cyclical movement 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, you take the case of your natural calamities your social unrest. In this case there is no trend of evidence has to create 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 may be it is a social unrest before 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 trend. So, there are 4 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 why that is pretty 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 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 4 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 or 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 we will see the series will plot a line we 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 50 and so on. So, suppose we have the data about last 5 years 2010 till 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 quantity. 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, 2006 this is 12, 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 discuss 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 b 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 of 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 graph in a 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 the 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 with the first differences we need to take the first 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, graphic so trend projection methods under quantity 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.