Forecasting - Exponential Smoothing

welcome again the next question we'll be doing is on forecasting the first part of forecasting that I will show you is called exponential smoothing it is again taken from January 2007 question number six part a question reads as follows emergency calls to the fire department over the past 15 years are as follows twenty twenty seven twenty five twenty to eighteen twenty one twenty six nineteen sixteen twenty eight twenty five twenty six seventeen twenty three and twenty seven use exponential smoothing with a smoothing constant of 0.5 to forecast the number of calls for the next week now how do we approach this question in doing forecasting it would be good to lay out a table the table we will lay out pretty much is as follows since we are dealing with weeks the first column will be week the calls the second column and the forecast would be the third now for week one the as they have given you an order week one would have twenty calls as we see the paper we see 20 27 25 22 18 what that means is that week once calls were twenty now this here 80 represents actual calls of at time T so what this means here is week one so the actual for week one is twenty the actual for week 2 which would be then what they call a two would be 27 this ft just represents forecasting for a particular period now what we are trying to find out is we have 15 weeks what the question is trying to find out is the forecasts for the 16th week which is f of 16 that's what we are trying to find out F of 16 now we're going to use this formula here which says f of T equals F of t minus 1 plus alpha open brackets actual of t minus 1 minus the forecasts of t minus 1 it looks very complicated but is actually very simple if you look at the back of your exam paper you see the form of sheet f of t means the forecast for a particular period f of t minus 1 t minus 1 means just the previous forecast alpha is the smoothing constant in this particular example alpha is given as zero point 5 a of t minus 1 just means actual of previous period f of t sorry minus f of t minus 1 just means minus the previous forecast now how do we apply it here now it's a very simple thing and I'll just show you so that you get the rhythm the first part of this question we actually have if there is no previous forecast given for period one which is your one we assume that the forecast for period one is equal to the actual for period one so before we start to use this formula here what we see since no forecast is given for the first period we assume that the actual for period one is the forecast for period one so in this case if the actual for period one was twenty before cast for period one will be twenty now we start the formula the formula we start like this we see F of 2 equals F of 2 let me do it here and then we'll transpose F of 2 equals F of 2 minus 1 would be obviously F 1 okay what's the previous forecast for period 2 would be period one's forecast plus alpha now actual of t minus 1 just means previous periods forecast which will be actual 1 minus the forecasts of 1 so when you want to forecast the second period you need the information from the first period that's all this formula is trying to say in a in the most simple way this is what it really means that for second period forecast you need the information from the first period now if I'm forecasting period 3 it says forecast for 3 f of 3 would be F of 3 minus 1 which is F of 2 plus alpha a remember this is forecast of 3 so it will be a 3-1 means actual for period 2 minus D forecast for period 2 you see a pattern now if you want to forecast the fourth period what you need is the forecast of the 3rd period plus alpha the actual of the 3rd period - the forecasts of the 3rd period now the rhythm goes like that once you get this F of 5 equals F of 4 plus alpha a of 4 minus F of four close bracket so as we transport that here the forecasts for period 2 is according to what we have just worked out F of 1 plus alpha a of 1 minus F of 1 now in this case here forecastle period to requires the forecasts of period one which I told you the first assumption would be if there is no forecast given there's no forecast given use the actual so that was the first assumption now second step forecast for period two equals F of one what is f of one this is week one F of 1 is 20 plus alpha now alpha was given as 0.5 this smoothing constant alpha means the smoothing constant it gives you as they give it you a 0.5 so it will be 0.5 open brackets actual of 1 what is the actual of 1 in this case 20 minus the forecast of 120 so in this case here will be 20 plus 0.5 20 minus 20 is 0 so this answer here is 20 so the forecast for period 2 is 20 so period 1 is 20 period 2 is 20 now we want to find period 16 in order to find period 16 we need period 15 but to find period 15 we need period 14 to find period for unique period 13s why we have to start from the top and come down next then F of 3 equals we have it here F of 2 plus alpha a of two plus sorry minus minus F of two now in this case here let's take the information again F of 2 is 20 plus alpha again is 0.5 open brackets now what is the actual for two actual for two if you come here is the actual calls that were made in week two which is twenty seven see that right got the 27 from actual for two is here the actual calls made in period two 27 - what was the for council period - 20 so what this is it is 20 plus 0.5 open brackets 20 minus 7 which is 20 plus 3 point 5 which equals twenty three point five okay now you have the rhythm now what you have to do now is work out F of four now I'm going to explain to you something when I'm doing F of four F of four means F of 3 plus alpha actual for 3 - forecast for 3 now in this case here what is the forecast for 3 we just worked it out here 23.5 plus 0.5 open brackets actual for 3 where's the actual for 325 - again the forecast for 325 0.5 let me see that now we need a calculator 0.5 1.5 we find that before cast 4 4 equals something yeah should I take a guess all right 23.5 plus 0.75 we're getting like twenty four point two five yeah twenty four point two five okay now what you need to do now is work out F of five F of six F of seven F of eight all the way down to F of 15 after you work out F of fifteen then you work out F of sixteen again F of sixteen is what the question is asking for what is the forecast for period 16 however in order to do it you have to first start from the top now advice for you when doing in your exam is you need to get a scientific calculator now scientific calculator especially the one that has brackets all scientific calculators should have brackets we we want to avoid using calculators looking like this we need a scientific calculator otherwise if you use calculators like this it can take you longer to do this question now in a scientific calculator what you find is that you can actually input this in one stroke in a scientific calculator you put 20 plus 0.5 open brackets 27-20 close brackets equals it will actually give you this answer right away then when you take this answer and put it into your next line you use your scientific calculator again to work it out it makes this calculation very quick using a scientific calculator and eye exam this question should take you no more than 15 minutes if you don't use a scientific calculator you can take you up to 45 minutes so to save time please use a scientific calculator here now after you have worked out again all of these steps up to F of 15 F of 16 will be your forecast for period 16 that is what the question is asking the question asks using exponential smoothing with a smoothing constant of 0.5 to forecast the number of calls for the next week the next week would in this case imply since it was 15 weeks you're looking for the forecast for period 16 now another way you can verify your answers especially if you're practicing this at home is at the back of your textbook as you can use this for all your for your all your exam questions at the back of the book there is a CD inside of that CD you install a program called quantitative it's called QM for Windows quantitative method for Windows you can install the version qm 2 or qm 3 when you install that program then you go inside the program and you go under for casting when you go under for casting you can input this information and calculate this question using exponential smoothing just play with the program if you're unsure on how to use a computer you can ask someone in your group to help you go through it but it's very simple to do through your computer program quantitative methods what I will be showing you in the next few minutes is the next part of that question which deals on trend projection thank you

Channel: romriodemarco

Views: 204,848

Keywords: CHSB, Exponential Smoothing, Forecasting, QBA

Id: hi3CoA9-hvg

Length: 15min 21sec (921 seconds)

Published: Fri Feb 01 2013