Quantitative and Qualitative Forecasting

462 section 4 St ppr.r rrn I)t.rtrlrr I't,tllNrlr; ,tNtr Cttltritit Fmne*ast err*r The difference between actual demand and what was forecast. Mean absolute deviation (MAD) The average of the absolute value of the actual forecast enor. error range, fbr this analysis, consisls of errors resulting iiom both lines as well as all other possihle lines. We included this exhibit to show ho,*' the effor rAnse widens as we so furlher into the future. S*r*{:;x$t Hrri:rg In using thc tcrm , wc arc rcf.crring to thc diffcrcncc bctwcen what actually occurred and wl.rat was fbrecasl. In statistics, ihese errors are called residuals. As long as thc lbrccast value is rvithin thc conficlcncc lirnits, as wc discuss later under thc hcading. "Measurement of Enclr," this is not really an cror sincc it is what we expected. But comnlon usage rel'ers to the difference as an error. Demand tbr a product is generated tl.rrough the interaction of a numbet'of l-actrlrs too coln- plex to descrihc accurately in a rnodel. Therefbre, all forecasts certainly colttain some clror. In discussing tbrecast errors, it is convenient to distinguish between sources ctf error and the measttretnenl of e rnt r. $o u rges sf H rro r Errorscan come from avariefyof sources. (Jne common source that many tbrecasters are unaware of is projccting past trencls into the future. For example. whel wc talk about statislical erLors in regression aualysis, we are rct-crring to thc deviations of observations from our regression line. It is common to attach a confidenco band (that is, statistical control limits) to the regression line to reduce the unexplained etror. But when we then use this regression l:ine as a fbrecasting device by projercting it into the fitture. the etror may not bc correctly definccl by tlie proiected contidence band. This is bccause the confidencc interval is basod u1 past data; it may not hold tbr projected data points and therclirre cannol' be used with thc same confidencc. In fact, experience has shown that the actual errors tend to be grcater than tliose predicted [l'om lbrecast models. Erors can be classifierj as bias or randclm. Bius errors occur when a cutsistent mistake is madc' sourccs ot'bias incltttlc thc iailurc to includc thc right variablcs: thc: usc tll'thc wrong relationships among variables; cmploying the wrong trend line; a mistaken shift in the sea- sonal demancl frorn where it normally occurs; ancl the cxistencc of somc unclctectcd sccular trend. Rantlorn errors can be defined iis those that cannot be explained by the forecast model being uscd. M e a s u re m €nt of E rrgr Scvcral common tcrms uscd to dcscrihe: thc dcgrccr of elTor arc standard error, nleen squared error (ot t,ariance), an(l mean absoltrte devittion. In a{clition. tracking signals may he used to indicate any positive or negative hias in the forccast- Standard eror is discussed in the section on linear regression in this chaptc'r. Becartse the stanriard errtlr is the square root of a tunction. it is often mu'e convenient to use the function itsclf. This is called the merur squared error. or variatlce. Tht: was in l'ogue in the past but subsequcntly was iglored in f-avor of standard deviation and standard error measures. In recent years, MAD has made a comeback bccause ol'its simplicity and usefulness in obtaining tracking signals. MAD is the average error in the forecasts. using absolute values. It is valuablc because MAD, like the stanclard deviaticln, measures the dispersion of some observed value iiom some ex- pected value. MAD is computod using the di{I'erences between the actual demand lrnd thc lbrecast de- rnancl rr,'ithoul regard to sign. It equals the sum of the abscllute deviations divided by the num- ber ol-clata points or, staled in equation {brm, !ra, * r, r MAD: *J--=r- where r - Pcriod numbcr A, : Actual demand fbr the period / Analytics [18.1{]