Quantitative and Qualitative Forecasting

a 460 rie( li0n :l Sr prrt lln L)t.rtrnu Pr.,tlxtrr;,t [-rtx'txrtt Decoffiposition UsinE Least Square$ Regres$ion This procedure is difl'erent from the previous one and in sotne cases may give better results. Thc approach described in Example 18.3 starlcd by fitting a regression line, and given the line, the seasonal indexes are calculated. With this approach rve start by calculating seasonal indexes; then using data that have been "deseasonalized" we estinrate a trend line using linear regression. More formally, the prclcess is: 1. Dccompose the timc scries into its components. tu. Find seasonal component. b. Deseasonalize the dernand. c. Find trend conlpurent. Forecast future values of each component. a. Project trcnd conrponent into Lhe l-uture. h. Multiply trend component by seasonal component Exhibit I 8. 1 1 shows the decomposition of a ti nre series using least squares regression and the same basic data lve lrsed in our flrst regression exanrple. Each data pttint corresponds ttr using a single threc-month quarter of the three-year (12-quarter) pcriod. Our objective is ttt forccast dcrnand for thc iotu'quartcrs of thc fburth ycar. Step 1. Determine the seasonal factor (or index). L,xhibit I 8. I I summarizes the calcula- tions needed. Column 4 develops an average tor the samc quarters in the three-year period. For cxat-nplc, thc lirst quaftcrs of thc threc ycars arc added togcthcr and dividcd by thrce. A seasonal factor is then derived by dividing that averago by the general average tbr all , .tt.l50 2.:66.7 ll quartl-rs (=# tr 2.7791. F..examplc, this tirst quzlrtcr seasonal l.actor is ## : 0.82. These are entered in column -5. Note that thc seasonal fhctors are identical 1br similar quarters in each year. Step 2, f)eseasonalize the original data. To removc thc scasonal efTcct on the data, wc dividc thc original data by the seasonal factor. This step is called the deseasonalization of dcrnand and is shown in column 6 of Exhibit l8.l I . Step 3. Develop a least squares regression line for the deseasonalized data. The pur- posc hcrc is to dcvclop an equation for thc trend linc /. which we thcn modity with thc scasonal factor. The procedure is the same as we used beibre: Y:a*bt where )', : Deseasonalizcd demand (see Exhibit -l8. t 1) / : Quartel' )' : Demand computed using the re-uression cquation Y : a * bt a : Iintcrccpt D : Slope of the line The least squares calc-ulations using colurnns l, 7, and li of Exhibit 18.1I are shown in the lower section ol'the exhibit. Thc flnal deseasonalized eqiration lirr our data is l' - -554.9 + 342.2t. This straight line is shown in Exhibit 18"12. Step 4. Project the regressinn line through the period to be forecast. Our purpose is to lirr"ecast periocls I 3 through I 6. We slart by solving thc equation lbr I at each ol' thesc periods (shown in step 5, column 3). )