INTRODUCTION TO FORECASTING

INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren daa). Forecass are used o improve decision-maing and planning. Even hough forecass are almos always in error, i is beer o have he limied informaion provided by a forecas han o mae decisions in oal ignorance abou he fuure. EXAMPLE: Demand (sales) forecasing -- Firms mus anicipae fuure demand o bes plan how o saisfy i hrough on-hand invenory or available capaciy. The producion or procuremen lead ime ofen requires producion and ordering decisions o be made before demand occurs. FORECASTING DECISION-MAKING ENVIRONMENTS: shor erm (0-6 monhs) <----------------> long erm (2+ years) operaional decisions sraegic decisions frequenly made infrequenly made low level of responsibiliy op managemen level individual iems produc line /\ /\ /\ weely demand annual (monhly) demand 10-year demand (invenory conrol) (producion planning) (faciliy planning) QUALITATIVE VS. QUANTITATIVE METHODS Qualiaive forecasing echniques (soliciing opinions): - subjecive, based on he opinion and judgmen of consumers, expers, managers, salespersons - appropriae when pas daa are unavailable (new produc) or when pas daa are no reliable predicors of he fuure - usually applied o inermediae -- long range decisions Quaniaive forecasing echniques: - explici mahemaical models are used o esimae fuure demand as a funcion of pas daa - appropriae when pas daa are available and also are reliable predicors of he fuure - usually applied o shor -- inermediae range decisions

QUALITATIVE FORECASTING METHODS 1. Informed opinion and judgmen: - subjecive opinion of one or more individuals - accuracy of he forecas depends on he individuals - EXAMPLE: ("grass roos") collecion and aggregaion of individual sales forecass o obain overall sales forecas by produc or region 2. Delphi mehod: an ieraive echnique for obaining a consensus forecas from a group of expers, wihou he problems inheren in group decision-maing (he "bandwagon" effec, influenial individuals). The procedure wors as follows: firs, give a se of quesions o each exper, who provides answers (forecass) independenly from he oher expers. The responses are colleced and numeric responses are saisically summarized. If a consensus was no obained, reurn he summarized responses o he expers, along wih any commens made by he expers (anonymously), and have hem revise heir forecass based on his daa. Repea unil eiher a consensus is reached (he answers converge) or else a "salemae" occurs (no convergence can be obained). - EX: long range forecasing of echnological advances 3. Mare research: Quesionnaires and inerviews are used o solici he of poenial cusomers, curren users, and ohers. One poenial problem is ha saed inenions (expecaions) do no always ranslae ino behavior. - EX: voer preferences, new car buyers 4. Hisorical Life-Cycle Analogy: Demand for a new produc can be forecas by anicipaing an S-shaped growh curve similar (analogous) o he S-curve experienced wih relaed producs PRODUCT LIFE CYCLE CURVE Sales per ime mauriy period (unis) decline growh inroducion ime

QUANTITATIVE FORECASTING TECHNIQUES TIME SERIES ANALYSIS: - Assumes ha paerns in demand are due o ime - Projecs pas daa paerns ino he fuure (exrapolaes from hisorical demand) Time Series Decomposiion: decompose (brea down) he paern ino level, rend, seasonal, cyclical, and random componens. - he random componen is, by definiion, unpredicable - he cyclical componen is due o long erm (several years) business/economic cycles and hus is very difficul o idenify - ime series mehods usually ry o idenify he seasonal (a cycle ha repeas yearly), rend, and level componens Time Series Mehods: F +1 = demand forecas for period +1 A = acual demand for period 1. Las period demand (ofen called he "naive" forecas) F +1 = A 2. Arihmeic Average: average of all pas demand, o "average ou" or "smooh ou" he random flucuaions F = +1 i=1 Ai = ( A 1+A 2+...+A ) / 3. Simple Moving Average (N-Period): average of he N mos recen demands, o "smooh ou" he random flucuaions -- he average "moves" o include he mos curren daa (in case demand really isn' fla) F = +1 i=+1-n Ai N Choosing he value of N involves a radeoff beween sabiliy (he abiliy o mainain consisency and no be influenced by random flucuaions) and responsiveness (he abiliy o adjus quicly o rue changes in he demand level): - large N means he average is sable bu less responsive o changes in demand - small N means he average is less sable bu will respond more quicly o changes in demand

4. Weighed Moving Average (N-Period): - The weighs are chosen so ha hey sum o 1 - If all weighs are equal (W i = 1/N for all i), he weighed moving average is equivalen o he simple moving average. +1 N F = W A i=1 i -i+1 - Advanage: can vary weighs o emphasize more recen daa - Disadvanage: o change responsiveness, mus change weighs individually; requires recording or soring N weighs and N pas demands 5. Simple Exponenial Smoohing: a simple way of calculaing a weighed moving average forecas wih exponenially-declining weighs; only he previous forecas, mos recen demand, F +1 = A + (1- )F, where 0 1 and he value of a smoohing consan are needed o calculae he new forecas. Anoher way of wriing he equaion clearly shows ha he new forecas is equal o he old forecas plus an adjusmen, where he adjusmen is calculaed as he smoohing consan imes F +1 = F + ( A - F ) he previous forecas error: The value of he smoohing consan, α, deermines how much of an adjusmen or correcion will be made in response o he mos recen demand. Large α means a larger adjusmen (more weigh given o recen daa, giving less sable and more responsive forecass), while small α means a smaller adjusmen (more weigh given o older daa, giving more sable and less responsive forecass). An equivalence (his only means he forecass will be similar, no idenical) beween an N-period simple moving average and an exponenially-smoohed average is obained by seing = 2/(N+1). The exponenial smoohing procedure yields a weighed moving average wih exponenially-declining weighs and an "infinie" number of erms (all pas demand daa bac o ime =1 is given a leas some weigh). The weighs given o he individual demands can be calculaed using he following formula (W 1 is he weigh given o he curren period's demand, W = (1- ) W 2 is he weigh given o he nex mos recen demand, and so on): -1

Example: =.1, F 1 = 100, A 1 = 105 Wha happens wih he exreme values of? Wih simple exponenial smoohing, he forecas for any period in he fuure (for example, he ph period beyond he curren period) is he same value: F +p = F +1, for p > 1. (I is liely ha his forecas will decline in accuracy he furher ino he fuure ha i is projeced.) 6.Calculaing Muliplicaive Seasonal Indexes: 1. collec monhly (quarerly) demand daa for several pas years 2. for each monh (quarer) of pas daa, calculae he raio of demand o a 4-quarer (12-monh) moving average 3. average he raios for several years of a given quarer (monh) o ge he seasonal index for ha quarer (monh) Example: Demand (000's of unis) 2002 2003 2004 Q1 1 2 2 Q2 3 4 5 Q3 5 6 7 Q4 3 3 4

EVALUATING FORECAST QUALITY Forecas error, or a relaed performance measure, can be used o selec a forecasing mehod ha has he smalles forecas error, and o monior he performance of a forecasing mehod in use. Error is he difference beween acual demand and forecas demand: error = A - F. The cumulaive error is ofen called he running sum of forecas errors (RSFE). The mean forecas error (MFE), ofen called average cumulaive error or bias, measures he endency of a forecasing model o consisenly overforecas or underforecas. RSFE = ( A - F ), MFE = BIAS = ( A - F ) / =1 If bias > 0, forecass consisenly are oo low, and If bias < 0, forecass consisenly are oo high. Ideally, bias will be close o zero. The primary drawbac o using bias alone o evaluae forecas qualiy is ha posiive and negaive errors end o cancel. A relaed performance measure ha does no have his problem is he mean absolue deviaion (MAD): The MAD is relaed o he sandard deviaion σ in ha for normally-disribued forecas errors, σ 1.25MAD. A hird forecasing performance measure is mean squared error (MSE): MAD = A - F / =1 MSE = ( A - F ) / =1 MSE has he same advanage over bias ha MAD has, namely, posiive and negaive errors do no cancel each oher ou. The difference beween MSE and MAD is ha MSE penalizes large errors much more han MAD does. To selec a forecasing mehod from several poenial models, one approach is o ae a series of acual hisorical daa (demand) and apply each model o he daa. The mehod ha yields he smalles MAD or MSE and has bias close o zero usually is he preferred mehod. To monior he performance of a forecasing model in use, a racing signal is ofen used: TS = RSFE MAD 2 =1 Ideally, he racing signal will be close o zero, bu values wihin a specified range (for example, -4 TS 4) are considered accepable. If he racing signal falls ouside of he accepable range (his may occur if he underlying demand paern has changed sharply), sop and rese he forecas. Some researchers feel ha simple exponenial smoohing wih racing signal conrol is beer han rend-adjused exponenial smoohing.

CAUSAL FORECASTING Causal forecasing is appropriae when here is a "cause and effec" relaionship beween one or more independen variables (he "cause") and a dependen variable (he "effec") such as demand or some oher variable ha is being forecas. Causal models have he poenial o predic urning poins in he demand funcion, somehing ha ime series models can no do. (Why?) The general approach o causal forecasing is: 1. collec hisorical daa 2. develop and validae he model 3. use he model o forecas Muliple regression analysis is one approach used o develop a causal forecasing model. I is imporan o noe ha regression implies dependence and no necessarily causaion, however, causaion does no have o be proven for a causal forecasing model o be used effecively. The general form for a muliple linear regression equaion is: Y c = a + b 1 X 1 + b 2 X 2 +... + b X Y c = calculaed (prediced) value of he dependen variable a = inercep (consan erm) X j = jh independen (predicor) variable b j = coefficien associaed wih he jh independen variable A compuer (or programmable calculaor) is used for calculaing he inercep (a) and slope (b) coefficiens. The poin (single value) forecas made wih his model is he value of Y c afer curren values for he X j 's have been insered. Before a causal forecasing model is used i mus be validaed. This means o chec wheher he model conains only variables ha significanly help mae an accurae forecas. Following he "principle of parsimony", he simples model (he one having he fewes variables) ha gives good resuls should be seleced. Larger models, wih more variables, will have a smaller bias componen (good) bu also resul in larger forecas variance (bad). Some facors ha help in validaing a causal model include: 1. R-SQUARE (r 2, he Coefficien of Deerminaion) measures he percenage of variaion in he daa ha is explained by he model. R-SQUARE can ae any value beween zero and one. Ideally, R-SQUARE will be close o one. Alhough a large R-SQUARE value is desirable, he model wih he larges R-SQUARE may no be he bes model. Each variable included in he model will conribue o R-SQUARE, so he model ha conains all variables being considered will have he larges R-SQUARE of any model. However, if some variables do no significanly conribue o he model, i is beer o drop hem from he model and selec a model wih a

slighly smaller R-SQUARE. 2. ADJUSTED R-SQUARE is a variaion of R-SQUARE ha penalizes for overfiing he model (including oo many variables), and herefore is useful for geing a feel for how many variables should be included. 3. To es he significance of each independen variable, eiher a -es or an F-es (or boh) should be performed. For our purposes, he -saisic will be sufficien evidence of he significance (or lac hereof) of a variable. The -es for a given variable uses he null hypohesis ha he coefficien of ha variable is equal o zero. A large -value (small PROB value) indicaes ha he null hypohesis should be rejeced, and hus he b i coefficien is liely o be non-zero and he variable should be included in he model. Conversely, a small -value (large PROB value) implies ha he null hypohesis should be acceped, and herefore he b i coefficien is no significanly differen from zero. In his laer case, he variable should no be included in he model. A general guideline for selecing and validaing a causal forecasing model is o (1) hin of all variables ha may help predic he iem being forecas and (2) collec hisorical daa for several observaions, where each observaion conains he value of he iem being forecas (for example, sales) as well as he values of he predicor variables (for example, he prime ineres rae) a he same poin in ime. Nex, he facors described above (R-SQUARE, ADJUSTED R-SQUARE, and he -ess) can be used o (3) examine each model in deail and deermine which variables should remain in he final model.

An Example of Causal Forecasing Using Muliple Regression Analysis The manager of a real esae firm in a large meropolian area wans o esablish a model for forecasing he mare value of residenial propery. She believes ha such a model would enable her firm o decrease he lengh of ime ha a clien's house remains on he mare, since he asing price would be more in line wih rue mare values. (1) The manager hins ha he mare value of a house may be influenced by four facors: he size of he house, he disance ha he house is from he business disric, he condiion of he house, and he size of he lo. (2) A random sample of 10 houses sold wihin he pas wo monhs generaed he following daa: [MV] [SQFT] [DIST] [COND] [LOTSIZE] Mare Value Size of House Disance from Condiion Size of Lo (selling price) (in square fee) Business Dis. of House (in acres) (in miles) (0-10) $ 50,000 1,200 6 7 0.5 $ 90,000 2,500 8 9 0.5 $ 72,000 3,000 5 5 2.0 $ 42,000 1,000 3 8 0.5 $ 120,000 3,500 25 10 10.0 $ 75,000 2,000 10 7 5.0 $ 35,000 1,000 2 6 1.0 $ 75,000 2,000 9 9 1.0 $ 60,000 1,500 8 8 5.0 $ 100,000 3,000 5 9 2.0