 Hello friends, we have seen what is forecasting, what are the methods of forecasting, what is the statistical method, simple regression we have studied in the last session. After the forecasting methods, we will be studying what are the various forecasting errors. At the end of the session, you will be able to investigate what are the forecasting errors and you will be able to calculate various forecasting errors with the given formula. We will have first introduction of errors, then we will be studying what are the various types of forecasting errors, mainly bias, mean absolute deviation, mean absolute percentage error, mean square error, tracking signals, okay. Forecasting errors, what is a forecasting error? We try to forecast with variety of methods, maybe Delphi technique or maybe statistical technique, even maybe using some of the latest software also. We try to find out from the past data what will be the projected figure for the future data and once actual data will come into the reality, we try to compare the forecasted value versus actual value and we will be seeing that there will be some difference between the forecasted and the actual data. The difference is known as error, the difference can be on the positive side or the difference can be on the negative side. Both errors are not a welcome situation from the organization point of view. Suppose if the actual data tells you that the sales demand has increased then the forecasting figure then probably we will be having a shortage in the market of our products and then probably that may be taken by some other customer that is not advisable. In the second case if the actual data falls short of the forecasted value that means we are selling less than the forecasted as a result of that we have invested into resources we have built up the build inventory and as a result of that we are unable to sell that will result into the inventory pile up maybe in some cases it may lead to stocks which will have inventory is sometimes maybe a dangerous situation it may block cash flow it may block capacity and sometimes if the product is not continued in the next quarter of the next period there are chances of obsolescence and damage to the product so in that case that also is not a welcome situation the basic purpose is we try to minimize the gap between the actual and the forecasted values the difference between the forecasted and actual value is generally called as the error the ultimate aim of all calculations all methodologies all approaches is tried to build at that error should be as minimum as possible as you know the forecast error is the difference between the actual and the forecasted value for the corresponding period in terms of a equation it can be written as e t is equal to y t minus f t where e is the forecasting error at period t y is the actual value at period t and f is the forecast for the period t there are number of methods forecasting error can be calendar forecast error or cross sectional forecast error when we want to summarize the forecast error or a group of units now forecasting is a very funny data interpretation as the forecasting period is longer the data the error will be more as the forecasting period will be shorter there will be a small error it also depends upon all geographical factors the calendar months the areas and units and the product mix and so on and so forth so forecasting error we can summarize it as per our requirement for which we want to date the data analysis and take further decisions from the data if you observe that average forecast error for the time series of the forecast for the same product or phenomena that we call this as a calendar forecast error or time series forecast error what is the meaning of this suppose if we take Diwali season or any festival season for this particular year take the similar sale and similar postcard value the corresponding earlier years then we take this as a calendar forecast error what was the error what was the actual sales data in the last festival last to last festival and based on that we will be able to calculate any forecasting this time then that error what was the error in the earlier period that is that error was called as calendar forecast error if you observe this for multiple products and for the same period then this is called as cross sectional performance error if you take the data for multiple products then becomes cross sectional performance error now what are the various types of forecasting errors we will study one by one the first and very simple preliminary error is called as generally bias bias indicates the directional tendency of the forecasting error the forecasting repeatedly over estimates actual demand bias will have positive value and under estimation will indicated by the negative value bias is equal to some of the forecasting period errors for all periods divided by number of periods that is forecasted demand minus actual demand upon n but to think now what is the meaning of bias is positive or 0 or bias can be negative also look at the definition and then try to find out answer for this simple question right positive bias means forecasted value is more than the actual demand it means that we have forecasted to a higher extent and the actual demand is less we are unable to sell as per the forecast as a result of that we may result we may comment to the conclusion that our products are having inventories ideally the bias should be 0 that is actual demand and forecasted value should be similar if the bias value is negative in that case forecasted value is less than the actual demand it means we will be having shortage of our products in the market as a result of that there are chances that we may lose our market to our competitors so on the one side positive bias will indicate more inventory on the negative side it will indicate shortages what is indication of all these biases bias is called as directional error if continuously for some period of time the bias should be positive trend or for a continuously trend the bias shows negative value then it is a matter of concern that we have to review and rethink how the method of calculating or forecasting and then probably it needs some correction natural tendency of plus minus is obvious statistical variations in the demand are obvious if plus minus is there we can correlate to the actual market demand and then market variations but continuity in the same positive or negative direction definitely calls for review in the forecasting method itself right now the second error is the mean absolute deviation which indicates on an average basis how many units the forecast is off from the actual data it is not taking the signatures or it is not taking positive or negative value it is taking absolute value that is why it is called as mean absolute deviation it is related as sigma into e t upon n where sigma t is absolute value of the error and the number of period of evaluation it generally tells what is the total absolute deviation it may be from the positive side or negative side further to it we can calculate mean absolute percentage error which indicates on an average how much percentage of the forecast is off from the actual data hence bias is directly giving in terms of the quantities whereas mean absolute percentage error will try to estimate error in terms of percentage what is the percentage is sigma e t divided by e t divided by n into 100 whereas sigma e t is the absolute value of the error and is the number of periods of evaluation and e t is the actual demand for the period t this will tell you the percentage error is 20 percent 30 percent 40 percent whatever the percentage may be the percentage will tell us how much we are deviating from our values percentage is not considering any negative or positive sign it may not indicate directional values as such third type of error generally which is calculated in the forecasting method is called as mean square error generally called as msc a forecast error measures that penalizes large error proportionately more than the small errors it is a method that we are trying to find out in a way we are giving some consideration for the large and small error proportionality large error is having more penalty as compared to small error it will generally a good indicator so as to take some corrective action on the forecasting method or on the further decisions based on the forecasting method it is generally represented as sigma e t square divided by n where e t is the value of error we are taking the square of the value of error and then we are dividing it by n is equal to number of periods tracking signal the ratio of cumulative forecasting errors to the corresponding value of the mad it monitors any forecast that have been made in comparison with the actual and once when there are unexpected departures of the outcome from the forecast so tracking signal is actual value minus forecasted value divided by mean absolute deviation so it tries to give a signal and whether you are on the track or right so depending upon the purpose we can use the method of calculating the error the proper method is used and then the ultimate purpose should be the error should be as minimum as possible now here is a small example where we have given some sales data and forecasted data and you have to calculate the various forecast errors the answer is given over here bias is minus 2 absolute mean absolute deviation 58 ms is 8 to 8 0 and then ma p is 2.64 similarly we can calculate the errors into the given data we can have alternative examples also based on this so this data will be useful for the interpretation of errors and taking right corrective actions thank you