FORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND

by

Watchareeporn ChaimongkolNational Institute of Development Administration,

Bangkok, ThailandEmail: watchare@as.nida.ac.th

and

Chutatip TansathitKing Mongkut's Institute of Technology Ladkrabang,

Bangkok, ThailandEmail: ktchutat@kmitl.ac.th

ABSTRACT

The objective of this study is to improve and develop forecasting model for automobile customer demandestimation. Automobile industries in Thailand are one of major industries, which contribute to the nation’s economy. The competition among car manufactures in Thailand is crucial. Thus, inventory management needs to be efficient.Currently, most dealers take orders based on prior sales to ensure that cars will be available to customers. However, if stocks are at dealers for a long time, it would pose a financial risk to the company. If we have a better forecasting model for demands, there should be fewer dead stocks. Therefore, we introduce a new model based on the modification of Decomposition and Holt-Winters’s forecasting model to estimate customer demand of passenger cars. Finally, we evaluate our forecasting model by comparing the forecasts with actual data. The percentage of mean absolute percentage error (MAPE) shown that the modified forecasts performed better than other methods for all groups of data under studied.

KEYWORDSInventory Management, Forecasting Model, Decomposition Method, Holt-Winters Method, Combination Forecasting Methods

INTRODUCTION

Worldwide automobile industry is growing at a rapid pace as many countries are going through the phase of economic development (Report Linker, 2007). Automobile industry in Thailand is one of major sectors, which significantly contributes to Thailand’s economy. In 2007, export values of automobile and parts were ranked at second for the contribution to Gross Domestic Products or GDP (Thailand Automotive Industry Association, 2007). Thus, Thai Government has been pushing Thailand to be the Detroit of Asia by intensively supporting through funds and taxscheme. As a result, this significantly increase the competition among car manufactures in Thailand, especially passenger cars. Nowadays, passenger car reliabilities are not significantly different among brands due to compliance to international standards.

Because of there are around 30 brands of passenger cars in Thailand and the top ten in 2009 were Toyota, Honda, Nissan, Mazda, Chevrolet, Mitsubishi, Proton, Ford, Suzuki, and Volvo (http://www.toyota.co.th/th/sale) . All of them aim to compete on price and assess their strengths and weaknesses to compare with the competitors. The manufacturer focus on reducing production cost to achieve competitive prices as well as to gain the profit. Usually, waste reduction considers about materials, production time and production inventory. For automobile sales, passenger car dealers take order based on prior sales data. If they overestimate the order quantities and inventory holding, the problemwill arise at the end of model life, because it is difficult to clear out pending inventory. Thus, it is essential to have accurate forecasting model for customer demand of passenger cars.

This paper proposes a developed forecasting model using the real data of sales passenger cars in Thailand during January 2007 to July 2010 to estimate customer demand. There are many forecasting techniques, such as, smoothing methods, classical decomposition, regression analysis, seasonal smoothing methods and Box-Jenkins methodology. In

order to develop the model, the “Decomposition method” and “Holt-Winters’ method” have been selected for this studybecause both of them are often applied to time series that exhibit trend and seasonality. After that, we evaluate this forecasting method by comparing the forecasts with the actual data. In addition, to evaluate the model, the error is analyzed using mean absolute percentage error (MAPE).

Forecasting Model

In related forecasting models, Decomposition model is discussed in section 2.1 and Holt-Winters model in section 2.2. In section 3 a model development is proposed.

Decomposition Model

Decomposition model is useful when the parameters describing a time series are not changing over time. These models have no theoretical basis, but they are strictly an intuitive approach. The basic idea is to decompose the time series into several factors: Trend, Seasonal, Cyclical, and Irregular (error). Estimates of these factors are used to describe the time series. Decomposition model can be classified into two types: Additive Decomposition model and Multiplicative Decomposition model (Bowerman B.L., et al. 2005).

Additive Decomposition Model

Additive Decomposition computes the decomposition of the time series into its components, which includestrend (T), seasonality (S), cyclical (C) and irregular (I). This model is useful for time series that exhibit constant seasonal variation. Whereas the parameters describing the time series are not changing over time, additive decomposition model is applicable to the time series.The model is

t t t t ty T S C I (1)

where T be the trend, S be seasonality, C be the cycle and I be the error.The p-step prediction equation is

ˆt p t t t ty T S C I (2)

Multiplicative Decomposition Model

Similar to Additive Decomposition, Multiplicative Decomposition computes the decomposition of the time series into its components, trend, seasonality, cyclical, and error and then projects to the future. The model is assumed to be multiplicative (that is, all parts are multiplied by each other to give the forecast). This model is useful for time series that exhibit increasing or decreasing seasonal variation.The model is

t t t t ty T S C I (3)

The p-step prediction equation is

ˆt p t t t ty T S C I (4)

Holt-Winters Method

Additive Holt-Winters Method

Suppose that the time series 1 2, ,..., ny y y has a linear trend locally with a level

( 0 ), a fixed growth rate ( 1 ), and has a fixed seasonal pattern ( tS ), with constant variation and the level, growth rate

and seasonal pattern may be changing over time. Then the time series may be described by the model

0 1t t ty t S (5)

(Bowerman, et al., 2005). The estimate tL for the level, the estimate tT for the growth rate, and the estimate tS for the

seasonal factor of the time series in time period t are given by the smoothing equations

1 11t t t s t tL y S L T (6)

1 11t t t tT L L T (7)

1t t t t sS y L S (8)

where , , and are smoothing constants between 0 and 1, 1tL and 1tT are estimates in time period 1t for the

level and growth rate, and t sS is the estimate in time period t s for the seasonal factor, and L is the length of

seasonality. The weight , , and can be selected by minimizing a measure of forecast error such as Mean Square

Error (MSE).

A point forecast made in time period t for p period into the future, t py , where 1, 2,...p is

ˆt p t t t s py L pT S (9)

where t s pS is the estimate of the seasonal factor for the season, corresponding to time period t p . To begin the

algorithm for equation (2) to (5), the initial value for the smoothed series tL , the Trend tT , and the seasonal indices tS

must be set by 1 1tL y , 1 0tT , and each of the seasonal indices are set to 1.0.

Multiplicative Holt-Winters Method

Suppose that the time series 1 2, ,..., ny y y has a linear trend locally, a seasonal

pattern, tS , with increasing (multiplicative) seasonal variation and the level, growth rate, and seasonal pattern may be

changing over time. Then the estimate tL for the level, the estimate tT for the growth rate, and the estimate tS for the

seasonal factor of the time series in time period t are given by the smoothing equations

1 11tt t t

t s

yL L T

S

(10)

1 11t t t tT L L T (11)

1tt t s

t

yS S

L

(12)

where , , and are smoothing constants between 0 and 1, 1tL and 1tT are estimates in time period 1t for the

level and growth rate, and t sS is the estimate in time period t s for the seasonal factor where L is seasonal period.

A point forecast made in time period t for p period into the future, t py , where 1,2,...p is

ˆt p t t t s py L pT S (13)

where t s pS is the estimate of the seasonal factor for the season corresponding to time period t p . To begin the

algorithm for equation (10) to (12), the initial value for the smoothed series tL , the Trend tT , and the seasonal indices

tS must be set by 1 1tL y , 1 0tT , and each of the seasonal indices are set to 1.0.

Model Development

The “Decomposition method” and “Holt-Winters’ method” have been selected to modify because both of them are often applied to time series that exhibit trend and seasonality. To combined two forecasts from Additivedecomposition model (equation (1)) and Additive Holt-Winters model (equation (5)), the forecasts are combined by using a constant coefficient regression method. Regression Weights computes weight values for the models in the table by regressing the series on the predictions from the models. The values in the Weights column are replaced by the estimated coefficients produced by this linear regression.

Thus,

ˆ ˆ ˆt 1 t,decomposition 2 t,Holt-WintersF = b Y +b Y (14)

After that, the error of a combined forecasted is computed from (14), where

ˆt t terror e Y F (15)

Then, the moving average for three periods of te , ,t MAe , is computed , where

1 2(3)3

t

t t te

e e eMA (16)

where n stands for total number of data.

Finally, the combined forecasts are adjusted with smoothing error, by adding (3)teMA to t̂F , so the modified

forecasts for passenger cars become*ˆ ˆ (3)

tt t eF F MA (17)

FORECASTING AUTOMOBILE SALES

In our models, we classify data into 4 groups according to the percentage of market share in 2009: Toyota (46.8), Honda (34.7), other brands (18.5), and all brands in Thailand (100.0).

FIGURE 1ACTUAL NUMBERS OF CARS SOLD MONTHLY FROM JANUARY 2007 TO JULY 2010

Figure 1 shows the pattern of four groups (Toyota, Honda, Other brands, and all brands) of time series data used in this study. It is found that the patterns of all brands, Toyota, and Honda are the same, but pattern of other brands isdifferent.

To develop the forecast demand of passenger cars in Thailand, first of all, sales of Toyota, Honda, Other brands,and all brands series were forecasted by additive decomposition and Holt-Winters method.

Since passenger cars sales time series has both trend and seasonal variation, the additive Holt-Winters model requires three smoothing constants, , , and to estimate level, trend and seasonal variation consequently. SAS

software was used to determine smoothing constant as shown in Table 1. The smoothing constants in Table 1 give minimum sum of square error.

TABLE 1SMOOTHING CONSTANTS OF ADDITIVE HOLT-WINTERS METHOD

Smoothing Constant for Holt-Winters Method

Time SeriesLevel

Estimate ( )

Trend Estimate ( )

SeasonalEstimate( )

Toyota 0.706 0.001 0.001

Honda 0.001 0.001 0.001

Other Brands 0.999 0.001 0.999

All Brands in Thailand 0.542 0.001 0.001

The results of forecasts from decomposition and Holt-Winters method with actual data for the four groups of automobile sales are shown in Figure 2.

FIGURE 2COMPARISON OF FORECASTS FROM DECOMPOSITION

AND HOLT-WINTERS METHOD WITH ACTUAL DATA

(Toyota) (Honda)

(Other Brands) (All Brands)

The results show that there are not better fitted of time series between Additive Decomposition and Additive Holt-Winters method. Hence, combination of two methods has been considered, using a constant coefficient regression method.

From regression analysis with SAS Program, we obtain four regression equations as follows:The regression equation for Toyota is

ˆ 0.2772( ) 0.7203( )ToyotaF Decomposition Additive H W (18)

The regression equation for Honda isˆ 154.57( ) 150.54( )HondaF Decomposition Additive H W (19)

The regression equation for other brands isˆ 0.0568( ) 0.094( )other brandsF Decomposition Additive H W (20)

The regression equation for all brands in Thailand is

ˆ 0.2443( ) 0.7557( )all brandsF Decomposition Additive H W (21)

After that, the errors of the combined forecasts were computed and the moving averages for three periods of errors were obtained. Finally, the modified forecasts were achieved by adjusted from (18) to (21) with smoothing errors. A comparison of forecasts from decomposition, Holt-Winters method and modified method with actual data for sales of all brands in Thailand is shown in Figure 3.

FIGURE 3COMPARISON OF FORECASTS FROM DECOMPOSITION, HOLT-WINTERS METHOD,

AND MODIFIED METHOD WITH ACTUAL DATA

(Toyota) (Honda)

(Other Brands) (All Brands)

MODEL EVALUATION

To evaluate the modified model, a criteria to measure the efficiency of the method in this study is Mean Absolute Percentage Error (MAPE), where

*

1

1

ˆnt t

nt t

y FMAPE

y

(22)

We used all the time series during January 2007 to July 2010 for model fitting. The percentage of mean absolute percentage error (MAPE), which classified by market share, comparing between the forecasts that automobile company came up with, additive decomposition, additive Holt-Winters, and our modified model are shown in Table 2.The percentage of MAPE showed that the modified forecasts performed better than other classical methods for all groups of data.

TABLE 2 MAPE OF THE CLASSICAL FORECASTS: ADDITIVE DECOMPOSITION, ADDITIVE HOLT-WINTERS,

AND A MODIFIED FORECASTS (ADJUST COMBINATION METHOD)

Percentage of MAPE

Time Series

Percentage of Market Share Additive Decomposition

MethodAdditive

Holt-Winters MethodModifiedMethod

Toyota 46.8 10.87 8.96 5.75

Honda 34.7

18.24 17.12 10.56

Other Brands 18.5 22.41 10.74 8.28

All Brands in Thailand 100.0 10.42 9.00 6.28

CONCLUSION

Because the Decomposition method and Holt-Winters method have a long time of application for forecasting demand of automobile in Thailand and the environment of automobile marketing changes every year, the forecasting method should be modified to create a new one with better forecasts. In performance evaluation, the modified method proposed in this study yielded less percentage of MAPE than those of additive decomposition and additive Holt-Winters method for all cases of data between January 2007 to July 2010.

REFERENCES

Available URL: http://www.toyota.co.th/th/sale_volum.asp?type_id=2&from_month=7&from_year=2010&to_month=8&to_year=2010&x=90&y=14

Bowerman B.L., O’Connell R.T. and Koehller A.B. (2005), Forecasting, Time Series, and Regression, 4th Ed, Thompson Learning, Inc.

Report Linker. Vietnam Automobile Industry Forecast (2007-2010). Available URL: http://www.reportlinker.com/p059590/Vietnam-Automobile-industry-forecast-2007-2010-.pdf.Thailand Automotive Industry Association, (2007), ‘Future Direction of Thailand Automobile Industries’, July 9th .