FORECAST OF CAR SALES IN BRAZIL THROUGH CLASSIC METHODS

Companies and industries seek models for their sales in order to predict future demand, so that they can obtain projections that enable improvements in planning, cost reduction and other benefits. In general, the projections resulting from forecasting models are based on historical data or on time series. There are several methodologies, techniques and forecasting models.

Among the most widespread methodologies in the literature, the following stand out: regression analysis, moving averages, classical decomposition, exponential smoothing, integrated autoregressive models and moving averages, Bayesian methods and neural networks.

With regard to regression analysis methods and their applications for making time series projections, one can refer to Gujarati (2006), while Gooijer & Hyndman (2006) present a relevant review of forecasting methods, in special exponential smoothing. The automatic forecasting methods presented by Box & Jenkins (1976) are widely disseminated, introduced in many statistical and econometric software, and known as ARIMA models.

Enders (2004) is another reference that must be cited for the mentioned classic models. Bayesian methods, in particular the dynamic models systematized in West & Harrison (1989), are quite useful for the development of forecasting models. The neural network methodology, which has shown significant development in recent decades, especially in forecasting time series, can be referenced by Zhang (2004).

The object of this study is the demand forecast for the automobile industry, which is relevant for planning the sector to take place in an organized manner after the recent financial crisis, which began in September 2008, which hit the entire world economy and, therefore, affected this sector of the Brazilian economy deeply.

Thus, this work seeks to study car sales in Brazil through classic forecasting methods, available in the literature, projecting the demand of the Brazilian car market as precisely as possible, based on information from the Associação Nacional dos Fabricantes de Veículos Automotores ( anfavea). This association brings together companies that manufacture motor vehicles with industrial facilities in Brazil, manufacturers of cars, light commercial vehicles, trucks, buses and self-propelled agricultural machinery. As the focus of this article is car sales, the data used here were monthly car sales in Brazil, from January 2000 to August 2009. The methodologies used in this work are based on linear regression analysis, on damping models exponential and in ARIMA models. Thus, this work seeks to study car sales in Brazil through classic forecasting methods, available in the literature, projecting the demand of the Brazilian car market as precisely as possible, based on information from the National Association of Motor Vehicle Manufacturers (Anfavea). This association brings together companies that manufacture motor vehicles with industrial facilities in Brazil, manufacturers of cars, light commercial vehicles, trucks, buses and self-propelled agricultural machinery. As the focus of this article is car sales, the data used here are monthly car sales in Brazil, from January 2000 to August 2009. The methodologies used in this work are based on linear regression analysis, on damping models exponential and in ARIMA models.

THE CAR MARKET IN BRAZIL

The Brazilian automobile industry has had several significant periods that represented a decline or increase in car sales, due to factors related, among others, to political changes and variations in the general level of prices. In September 2008, when the most recent global financial crisis broke out, the drop in sales was 15%. In an attempt to encourage the production of the automobile industry, the Federal Government sought to facilitate the purchase of vehicles by reducing the Tax on Industrialized Products (IPI).
Figure 1 shows the main facts of the Brazilian automobile industry.

APPLICATION OF FORECAST MODELS AND ANALYSIS OF OBTAINED RESULTS

The monthly car sales data in Brazil were used in the composition of two time series, one based on the real data of this market, represented in the graph of Figure 2. In the same figure, it is possible to observe a significant growth of car sales from 2005 and movements in sales in some periods, among which the movement caused by the 2008 crisis stands out.

The other time series was composed based on the variation in sales in the car market, calculated through the logarithm of the ratio of sales in period t, or current period, by period t -1, or previous period, calculated by the expression below, where Y represents the sale, and represented in the graph of Figure 3.

It should be noted that the time series of sales variation, in Figure 3, represents a stationary series for the mean, which cannot be inferred from the sales series in the graph in Figure 2. The time series analysis methods can be classified for analysis in stationary and non-stationary series. Given the importance of stationarity for a study of a stochastic process, there are several methods to test the hypothesis of stationarity of a time series. It identifies the presence of movements or the trend component in the series.

The test used to test the stationarity of the two time series presented in this work was the unit root test, called the Augmented Dickey & Fuller stationarity test, or ADF test. For a detailed description of stationarity tests one can refer to Gujarati (2006) and Enders (2004). After testing the series, the inferences made from the graphs were confirmed.

In order to carry out the car demand forecast, models were built for two series presented here, based on regression analysis, simple linear regression; in exponential smoothing, Holt's method and Winters' method; and in the methodology of Box & Jenkins, or the ARIMA models. The results obtained are presented below.

The result of the simple linear regression model for the sales series, the only estimated regression model, with time as the explanatory variable, obtained an explanation coefficient of 83%, while the standard error of the regression and the F statistic of the analysis of variance were 27236,35 and 560,97, respectively.
From these results it can be inferred that sales can be explained by this model, but other models should be investigated.

Thus, the Holt and Winters exponential smoothing models were estimated, using the sales series and the sales variation series. As previously mentioned, in addition to these models, the ARIMA models were estimated. Of the ARIMA models estimated for the two series studied, the one that presented the best results was the SARIMA, an ARIMA model that takes into account the seasonality of the information.
For the sales series, the model that presented the best fit was a SARIMA (0,0,4)(0,1,1), while for the sales variation series the selected model was a SARIMA (0,0,0 ,1,0,1)(XNUMX).

Based on the results obtained from the estimated models, Table 1 was created to compare the results and select the best model for predicting car sales in Brazil. The performance measures of the models listed in this table are as follows:
mean square error or mean square error (MSE); prediction sum of squares (PRESS); Akaike model selection criterion (AIC); Schwarz model selection criterion (BIC); and mean percentage error (MAPE).

After analyzing Table 1, it can be seen that the model based on regression analysis is the one that presents the least satisfactory results. This result was expected, as the model does not capture the trend and seasonality behavior presented by the data. It should be noted that only the sales series was used for the regression model.

On the other hand, it can be verified that the models built from the suggested methodology, initially Box & Jenkins (1976), were the ones that presented the best performances, as highlighted in Table 1. Among these, the model that presented the best performance for automobile forecasting in Brazil is the SARIMA (0,0,0) (1,0,1), estimated using the sales variation series. The graph shown in Figure 5 shows the sales variation data and the forecasts made using the SARIMA model.

Once the SARIMA (0,0,0)(1,0,1) model was selected, estimated from the data obtained through a logarithmic variation, the sales forecast was calculated for the following months of 2009 and 2010, as shown the graph shown in Figure 6, with the continuation of the series. The estimated values, or projections, can be seen in Table 2.

FINAL CONSIDERATIONS

The study did not consider the effect of the IPI reduction, which caused an increase in vehicle sales in 2009. Comparing the forecast result with the model chosen for the end of 2009 and for the year 2010 with the data real market, there is a variation of approximately 10% of MAPE in relation to the period from September to December 2009, compatible with the forecast error of the model for the historical series from January 2000 to August 2009, of 9,9, 17%; and approximately 2010% for the period from January to August XNUMX.

This error is attributed to the failure to consider the IPI increase for the year 2010, which implies the forecast of a higher volume of sales for that year. To take into account the IPI reduction or other qualitative characteristics in a future work, dummy variables could be used, in the case of classic methods, or interventions or discounts could be made, in the case of Bayesian methods. developed from this work are complemented with the use of classic autoregressive vector models and, mainly, Bayesian models. In addition, other methodologies can be considered, such as neural networks and fuzzy logic.

It is hoped that the results presented may contribute in an unpretentious way to studies of production planning and control in the automobile industry, an important sector of the Brazilian economy.

BIBLIOGRAPHIC REFERENCES

BOX, GEP; JENKINS, GM. Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day. 1976.
ENDERS, W. Applied Econometric Time Series. 2nd ed.
New York: Wiley, 2004.
GOOIJER, J.; HYNDMAN, R.. 25 Years of Time Series Forecasting, International Journal of Forecasting. v. 22, pp. 443 473, 2006.
GUJARATI, D.. Basic Econometrics. 4th edition. New York:
McGraw-Hill, 2003.
HARRISON, PJ; WEST, M. Bayesian Forecasting and Dynamic Models. New York: SpringerVerlag, 1989.
ZHANG, G.. Neural Networks in Business Forecasting.
London: Idea Group, 2004.
Anfavea consulted website:http://www.anfavea.com.br>. Accessed on 21/11/2009 and 20/10/2010.