FORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND

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1 FORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND by Wachareepor Chaimogkol Naioal Isiue of Developme Admiisraio, Bagkok, Thailad ad Chuaip Tasahi Kig Mogku's Isiue of Techology Ladkrabag, Bagkok, Thailad ABSTRACT The objecive of his sudy is o improve ad develop forecasig model for auomobile cusomer demad esimaio. Auomobile idusries i Thailad are oe of major idusries, which coribue o he aio s ecoomy. The compeiio amog car maufacures i Thailad is crucial. Thus, iveory maageme eeds o be efficie. Currely, mos dealers ake orders based o prior sales o esure ha cars will be available o cusomers. However, if socks are a dealers for a log ime, i would pose a fiacial risk o he compay. If we have a beer forecasig model for demads, here should be fewer dead socks. Therefore, we iroduce a ew model based o he modificaio of Decomposiio ad Hol-Wiers s forecasig model o esimae cusomer demad of passeger cars. Fially, we evaluae our forecasig model by comparig he forecass wih acual daa. The perceage of mea absolue perceage error (MAPE) show ha he modified forecass performed beer ha oher mehods for all groups of daa uder sudied. KEYWORDS Iveory Maageme, Forecasig Model, Decomposiio Mehod, Hol-Wiers Mehod, Combiaio Forecasig Mehods INTRODUCTION Worldwide auomobile idusry is growig a a rapid pace as may couries are goig hrough he phase of ecoomic developme (Repor Liker, 2007). Auomobile idusry i Thailad is oe of major secors, which sigificaly coribues o Thailad s ecoomy. I 2007, expor values of auomobile ad pars were raked a secod for he coribuio o Gross Domesic Producs or GDP (Thailad Auomoive Idusry Associaio, 2007). Thus, Thai Goverme has bee pushig Thailad o be he Deroi of Asia by iesively supporig hrough fuds ad ax scheme. As a resul, his sigificaly icrease he compeiio amog car maufacures i Thailad, especially passeger cars. Nowadays, passeger car reliabiliies are o sigificaly differe amog brads due o compliace o ieraioal sadards. Because of here are aroud 30 brads of passeger cars i Thailad ad he op e i 2009 were Toyoa, Hoda, Nissa, Mazda, Chevrole, Misubishi, Proo, Ford, Suzuki, ad Volvo (hp:// All of hem aim o compee o price ad assess heir sreghs ad weakesses o compare wih he compeiors. The maufacurer focus o reducig producio cos o achieve compeiive prices as well as o gai he profi. Usually, wase reducio cosiders abou maerials, producio ime ad producio iveory. For auomobile sales, passeger car dealers ake order based o prior sales daa. If hey overesimae he order quaiies ad iveory holdig, he problem will arise a he ed of model life, because i is difficul o clear ou pedig iveory. Thus, i is esseial o have accurae forecasig model for cusomer demad of passeger cars. This paper proposes a developed forecasig model usig he real daa of sales passeger cars i Thailad durig Jauary 2007 o July 2010 o esimae cusomer demad. There are may forecasig echiques, such as, smoohig mehods, classical decomposiio, regressio aalysis, seasoal smoohig mehods ad Box-Jekis mehodology. I

2 order o develop he model, he Decomposiio mehod ad Hol-Wiers mehod have bee seleced for his sudy because boh of hem are ofe applied o ime series ha exhibi red ad seasoaliy. Afer ha, we evaluae his forecasig mehod by comparig he forecass wih he acual daa. I addiio, o evaluae he model, he error is aalyzed usig mea absolue perceage error (MAPE). Forecasig Model I relaed forecasig models, Decomposiio model is discussed i secio 2.1 ad Hol-Wiers model i secio 2.2. I secio 3 a model developme is proposed. Decomposiio Model Decomposiio model is useful whe he parameers describig a ime series are o chagig over ime. These models have o heoreical basis, bu hey are sricly a iuiive approach. The basic idea is o decompose he ime series io several facors: Tred, Seasoal, Cyclical, ad Irregular (error). Esimaes of hese facors are used o describe he ime series. Decomposiio model ca be classified io wo ypes: Addiive Decomposiio model ad Muliplicaive Decomposiio model (Bowerma B.L., e al. 2005). Addiive Decomposiio Model Addiive Decomposiio compues he decomposiio of he ime series io is compoes, which icludes red (T), seasoaliy (S), cyclical (C) ad irregular (I). This model is useful for ime series ha exhibi cosa seasoal variaio. Whereas he parameers describig he ime series are o chagig over ime, addiive decomposiio model is applicable o he ime series. The model is y T S C I (1) where T be he red, S be seasoaliy, C be he cycle ad I be he error. The p-sep predicio equaio is yˆ p T S C I (2) Muliplicaive Decomposiio Model Similar o Addiive Decomposiio, Muliplicaive Decomposiio compues he decomposiio of he ime series io is compoes, red, seasoaliy, cyclical, ad error ad he projecs o he fuure. The model is assumed o be muliplicaive (ha is, all pars are muliplied by each oher o give he forecas). This model is useful for ime series ha exhibi icreasig or decreasig seasoal variaio. The model is y T S C I (3) The p-sep predicio equaio is yˆ p T S C I (4) Hol-Wiers Mehod Addiive Hol-Wiers Mehod Suppose ha he ime series y1, y2,..., y has a liear red locally wih a level ( 0 ), a fixed growh rae ( 1), ad has a fixed seasoal paer ( S ), wih cosa variaio ad he level, growh rae ad seasoal paer may be chagig over ime. The he ime series may be described by he model 0 1 y S (5) (Bowerma, e al., 2005). The esimae L for he level, he esimae T for he growh rae, ad he esimae seasoal facor of he ime series i ime period are give by he smoohig equaios L y S 1 L T (6) s 1 1 S for he

3 1 1 T L L T (7) 1 1 S y L Ss (8) where,, ad are smoohig cosas bewee 0 ad 1, L 1 ad T 1 are esimaes i ime period 1 for he level ad growh rae, ad S s is he esimae i ime period s for he seasoal facor, ad L is he legh of seasoaliy. The weigh,, ad ca be seleced by miimizig a measure of forecas error such as Mea Square Error (MSE). where s p A poi forecas made i ime period for p period io he fuure, y p, where p 1, 2,... is y L pt S ˆ p s p S is he esimae of he seasoal facor for he seaso, correspodig o ime period p algorihm for equaio (2) o (5), he iiial value for he smoohed series (9) L, he Tred mus be se by L 1 y1, T 1 0, ad each of he seasoal idices are se o 1.0. Muliplicaive Hol-Wiers Mehod Suppose ha he ime series y1, y2,..., y has a liear red locally, a seasoal. To begi he T, ad he seasoal idices paer, S, wih icreasig (muliplicaive) seasoal variaio ad he level, growh rae, ad seasoal paer may be chagig over ime. The he esimae L for he level, he esimae T for he growh rae, ad he esimae S for he seasoal facor of he ime series i ime period are give by he smoohig equaios y L 1 L 1 T 1 (10) Ss T L L 1 T (11) 1 1 y S 1 Ss L where,, ad are smoohig cosas bewee 0 ad 1, L 1 ad T 1 are esimaes i ime period 1 for he level ad growh rae, ad S is he esimae i ime period s for he seasoal facor where L is seasoal period. where s p s A poi forecas made i ime period for p period io he fuure, p ˆ p s p y, where p 1,2,... is (12) y L pt S (13) S is he esimae of he seasoal facor for he seaso correspodig o ime period p algorihm for equaio (10) o (12), he iiial value for he smoohed series S mus be se by L 1 y1 Model Developme L, he Tred, T 1 0, ad each of he seasoal idices are se o 1.0. S. To begi he T, ad he seasoal idices The Decomposiio mehod ad Hol-Wiers mehod have bee seleced o modify because boh of hem are ofe applied o ime series ha exhibi red ad seasoaliy. To combied wo forecass from Addiive decomposiio model (equaio (1)) ad Addiive Hol-Wiers model (equaio (5)), he forecass are combied by usig a cosa coefficie regressio mehod. Regressio Weighs compues weigh values for he models i he able by regressig he series o he predicios from he models. The values i he Weighs colum are replaced by he esimaed coefficies produced by his liear regressio.

4 Thus, F ˆ ˆ ˆ = b1y,decomposiio +b2y,hol-wiers (14) Afer ha, he error of a combied forecased is compued from (14), where The, he movig average for hree periods of e e e 3 where sads for oal umber of daa. error e Y Fˆ (15) e, e, MA, is compued, where 1 2 MA e (3) (16) Fially, he combied forecass are adjused wih smoohig error, by addig MA e (3) o F ˆ, so he modified forecass for passeger cars become ˆ * F Fˆ MA (3) (17) e FORECASTING AUTOMOBILE SALES I our models, we classify daa io 4 groups accordig o he perceage of marke share i 2009: Toyoa (46.8), Hoda (34.7), oher brads (18.5), ad all brads i Thailad (100.0). FIGURE 1 ACTUAL NUMBERS OF CARS SOLD MONTHLY FROM JANUARY 2007 TO JULY 2010 Figure 1 shows he paer of four groups (Toyoa, Hoda, Oher brads, ad all brads) of ime series daa used i his sudy. I is foud ha he paers of all brads, Toyoa, ad Hoda are he same, bu paer of oher brads is differe. To develop he forecas demad of passeger cars i Thailad, firs of all, sales of Toyoa, Hoda, Oher brads, ad all brads series were forecased by addiive decomposiio ad Hol-Wiers mehod. Sice passeger cars sales ime series has boh red ad seasoal variaio, he addiive Hol-Wiers model requires hree smoohig cosas,,, ad o esimae level, red ad seasoal variaio cosequely. SAS sofware was used o deermie smoohig cosa as show i Table 1. The smoohig cosas i Table 1 give miimum sum of square error.

5 TABLE 1 SMOOTHING CONSTANTS OF ADDITIVE HOLT-WINTERS METHOD Time Series Level Esimae ( ) Smoohig Cosa for Hol-Wiers Mehod Tred Esimae ( ) Seasoal Esimae( ) Toyoa Hoda Oher Brads All Brads i Thailad The resuls of forecass from decomposiio ad Hol-Wiers mehod wih acual daa for he four groups of auomobile sales are show i Figure 2. FIGURE 2 COMPARISON OF FORECASTS FROM DECOMPOSITION AND HOLT-WINTERS METHOD WITH ACTUAL DATA (Toyoa) (Hoda) (Oher Brads) (All Brads) The resuls show ha here are o beer fied of ime series bewee Addiive Decomposiio ad Addiive Hol-Wiers mehod. Hece, combiaio of wo mehods has bee cosidered, usig a cosa coefficie regressio mehod. From regressio aalysis wih SAS Program, we obai four regressio equaios as follows: The regressio equaio for Toyoa is F ˆ ( Decomposiio ) ( Addiive H W ) (18) Toyoa The regressio equaio for Hoda is F ˆ ( ) ( ) Hoda Decomposiio Addiive H W (19) The regressio equaio for oher brads is F ˆ ( Decomposiio ) 0.094( Addiive H W ) (20) oher brads The regressio equaio for all brads i Thailad is

6 Fˆ ( Decomposiio) ( Addiive H W ) (21) all brads Afer ha, he errors of he combied forecass were compued ad he movig averages for hree periods of errors were obaied. Fially, he modified forecass were achieved by adjused from (18) o (21) wih smoohig errors. A compariso of forecass from decomposiio, Hol-Wiers mehod ad modified mehod wih acual daa for sales of all brads i Thailad is show i Figure 3. FIGURE 3 COMPARISON OF FORECASTS FROM DECOMPOSITION, HOLT-WINTERS METHOD, AND MODIFIED METHOD WITH ACTUAL DATA (Toyoa) (Hoda) (Oher Brads) (All Brads) MODEL EVALUATION To evaluae he modified model, a crieria o measure he efficiecy of he mehod i his sudy is Mea Absolue Perceage Error (MAPE), where ˆ * y F MAPE (22) y 1 1 We used all he ime series durig Jauary 2007 o July 2010 for model fiig. The perceage of mea absolue perceage error (MAPE), which classified by marke share, comparig bewee he forecass ha auomobile compay came up wih, addiive decomposiio, addiive Hol-Wiers, ad our modified model are show i Table 2. The perceage of MAPE showed ha he modified forecass performed beer ha oher classical mehods for all groups of daa.

7 TABLE 2 MAPE OF THE CLASSICAL FORECASTS: ADDITIVE DECOMPOSITION, ADDITIVE HOLT-WINTERS, AND A MODIFIED FORECASTS (ADJUST COMBINATION METHOD) Time Series Perceage of Marke Share Perceage of MAPE Addiive Decomposiio Addiive Mehod Hol-Wiers Mehod Modified Mehod Toyoa Hoda Oher Brads All Brads i Thailad CONCLUSION Because he Decomposiio mehod ad Hol-Wiers mehod have a log ime of applicaio for forecasig demad of auomobile i Thailad ad he evirome of auomobile markeig chages every year, he forecasig mehod should be modified o creae a ew oe wih beer forecass. I performace evaluaio, he modified mehod proposed i his sudy yielded less perceage of MAPE ha hose of addiive decomposiio ad addiive Hol-Wiers mehod for all cases of daa bewee Jauary 2007 o July REFERENCES Available URL: hp:// x=90&y=14 Bowerma B.L., O Coell R.T. ad Koehller A.B. (2005), Forecasig, Time Series, ad Regressio, 4 h Thompso Learig, Ic. Ed, Repor Liker. Vieam Auomobile Idusry Forecas ( ). Available URL: hp:// Thailad Auomoive Idusry Associaio, (2007), Fuure Direcio of Thailad Auomobile Idusries, July 9 h.