Forecasting sales and intervention analysis of durable products in the Greek market. Empirical evidence from the new car retail sector.

Transcription

1 Forecasting sales and intervention analysis of durable products in the Greek market. Empirical evidence from the new car retail sector. Maria K. Voulgaraki Department of Economics, University of Crete, Greece 19 May, 2013 Abstract The Great Recession in Europe and the Greek economic crisis in the last five years and their impact the new car sales market, are the main focus of our analysis. This research paper tries to analyse, model and investigate the intervention impacts on new car sales levels and evaluate the accuracy of various forecasting techniques to predict car demand before and after the inclusion of intervention events (recession of the Greek economy), for a couple of car representatives operating in the Greek car market. The forecasting methods used in this study include: 1) simple Naïve, 2) seasonal Naïve models, 3) seasonal Autoregressive Integrated Moving Average (SARIMA) models, and 4)Exponential Smoothing State Space (ETS) models. Data on car sales are treated as time series observations and indicate the actual number of monthly new car registration numbers officially recorded in Greece, from January 1998 to December The data are obtained from the Greek Association of Motor Vehicle Importers - Representatives (AMVIR) statistical data base. The research focus on different Motor Vehicle importers- representatives operating in the Greek auto mobile retail market. Two different firms (Toyota and Opel), out of 10 included in the final research, are presented in this summary paper in order to display the forecasting process and the conclusions of this survey. This study focuses on the importance for forecasting accuracy of allowing for intervention events in the modelling process. All models are estimated both with and without intervention effects in an out-of-sample forecasting experiment for two different periods. Forecasting accuracy is assessed using two standard average loss functions defined as: the Root Mean Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE). Results show the importance of different models for forecasting car demand levels of each car representative for the two chosen periods. Additionally this research gives evidence that the implementation of the austerity measures in Greece during the period had negative impacts on new car demand in the Greek market place. Keywords: Time Series forecasting, Intervention impacts, Seasonal ARIMA models, Exponential Smoothing (ETS) models, car sales Maria K. Voulgaraki, Phd candiate in Economic Science in the field of Applied Econometrics, Department of Economics, University of Crete, Greece. mvoulgaraki@uoc.gr tel Supervisor:Prof. D.Tserkezos, Dr. G. Tsiotas, Department of Economics, University of Crete. 1

2 1 Introduction The Greek economic crisis and the financial agreement of the Greek government with the International Monetary Fund (IMF) gave rise to a deep recession phase in the Greek market that started in early This phase became even worse since May 2010 after the announcement of the financial agreement of the Greek government with the eurozone countries and the IMF on a bailout loan for the country, conditional on the implementation of austerity measures. The euro area Member States and the IMF have been providing financial support to Greece through an Economic Adjustment Programme and the release of the disbursements were based on observance of quantitative performance criteria and the positive evaluation of progress made with respect to policy criteria initially detailed in Council Decision 2001/734/EU of 12 July 2011 (as amended in November 2011, 13 March and 4 December 2012) and the Memorandum of Understanding setting the economic policy conditionality (with the last update signed on 7 December 2012). The impact of austerity measures in consumption were dramatic. Consumers postpone or prolong the purchase of durable products, like cars and therefore new car sales levels turned down reaching the lowest level ever recorded in the Greek market. The impact of recession, on the new car sales levels, in the Greek retail market and how sales can be modelled and analysed is the focus of this study. Firstly, we point out the importance for forecasting accuracy of allowing for intervention events in the modelling process by estimating all models both with and without intervention effects and generate forecasts for one year ahead. Two periods are estimated for each model: period (A)January December 2007 and period (B) January December 2010 generating out-of-sample forecasts for: (A) 2008 and (B) 2011 respectively. Secondly, the focus of this study is to examine the impact on car demand, for a sample of automobile retail firms operating in the Greek market, and how their sales level can be evaluated, modelled and forecasted. There is not much research on car sales level forecasting in Greece. Generally there are some papers for forecasting car sales demand in the American automobile market with the use of disaggregate choice models (Berkovec, 1985), forecasting automobile sales in connection to many economic and demographic variables (Shahabuddin, 2009). However in this empirical research we treat our data as time series data and include forecasting methods used in time series analysis, like the Naïve, the Seasonal Autoregressive Integrated Moving Average (SARIMA) models (Franses,1991, Greene,1993, Hamilton 1994), and the Exponential Smoothing State Space (ETS) models(hyndman et al 2008) while we include intervention analysis in the sample data (Chen, 2006). This summary paper continues by a brief analysis of the data with a graphical presentation of several plots and an illustration of a table with descriptive statistics. Then the forecasting models are specified alone with the accuracy measures used in this study. Lastly, the empirical evidence are presented together with the concluding remarks of the study. 2

3 2 Data The dataset used in this study consists of monthly car registration numbers officially recorded by the Greek authorities. The Greek Association of Motor Vehicle Importers - Representatives (AMVIR) statistical data base provide us the detailed information needed for all car representatives operating in Greece ( Data on monthly new car registration officially recorded by the Greek authorities are equivalent to new car sales in the retail market. The time period recorded starts from January 1998 and ends in December Time series data from different Motor Vehicle importers representatives, which operating in the Greek auto mobile retail market, are analysed. For convenience, the sample of this summary paper includes only two (2) different firms. They are selected from a group of ten (10) retail firms of the final research study. Both, Toyota and Opel, have two of the highest monthly sales levels in the Greek car market. Toyota had a rapid increase of their new car sales level for 2 years ( ) and then maintain a stable high market share in sales with very small upward and downward movements throughout the next years up until After 2010 the firm had a rapid downfall in new car sales until the end of Opel new car sales had been increasing rapidly from 1998 until 2001 but then stated falling until The company managed to regain its market share in 2005 but sales decreased again. In 2007 the company had managed to regain sales level at a lower but more stable level and kept it stable for the next two years. Unfortunately after 2009 the company had started a downfall movement on its sales level that became dramatic during and after Table 1: Descriptive Statistics for monthly new-car sales series simple and log-values. Descriptive statistics (1998:1-2011:12) OPEL TOYOTA Level Log Level Log Mean , ,48 Median , ,55 Max , ,28 Min 384 5, ,67 Standard Deviation 624 0, ,44 Skewness 0,28-0,63 0,14-1,07 Kurtosis -0,51 0,06-0,05 1,35 Jarque Bera test 3, 73 11,04 0, 54 45,42 Shapiro Wilk s test 0, 98 0,96 0, 98 0,93 Dickey-Fuller Tests -4,06-3,98-3,88-0,40 Note: One or two asterisks denote significance of tests at 5% or 1% levels. More details are given in Table 1 where descriptive statistics are reported for the total sample period. Jarque Bera test for normality in raw and in log value series of new car sales rejects the null hypothesis that the series are normally distributed only in the case of the log series. So the raw data seem to be normally distributed and the same result is supported also with the Shapiro Wilk test. The Augmented Dickey Fuller (ADF) unit root test gives evidence of stationarity only for the log values of the two series. Therefore, we proceed our research using the log values of both sample data. 3

4 (a) New car sales (b) Log new car sales (c) Decomposition of log new car sales Figure 1: Monthly new car sales in Greek market(1998:1-2011:12) Note:The graphs in this figure present in panel (a)monthly number of new car sales, in panel (b) log sales and in panel (c) Decomposition of the log series for Opel (in the left panel) and for Toyota (in the right panel). 4

5 3 Forecasting Models Forecasting methods do not exploit the understanding of time series behaviour as economic values but are rather interested in building simple models which capture the time series behaviour of the data and may be used to provide an adequate basis for predicting the series in the future (Hall, 1994). Table 2 briefly illustrate the forecasting models, while Table 3 illustrate the measures of forecasting accuracy for periods : A. January 1998 till December 2007 forecast 2008 B. January 1998 till December 2010 forecast 2011 The first period covers ten (10) years of quite stable Greek economy, while the second period covers thirteen (13) years, including a period of 3 years ( ) with dramatic changes in the Greek economy. The forecasting methods used in this research are: 1. Simple Naïve Method. In Naïve forecasting method the next step forecasts value of this period (t) equal to the observed value of the last period (t-1). Empirical evidence show that this method works remarkably well for many economic and financial time series especially in the short run predictions (Makridakis et al, 1998).This is happening as a consequence in an efficient market. 2. Seasonal Naïve Method. In Seasonal Naïve forecasting Method we just add the seasonal component to the previous Naïve forecasting method. Thus, the forecast value equals to the last value from the same period of time. In other words, when having monthly data the forecast for future January value equals to the last observed January value (Hyndman and Athanasopoulos, 2012). 3. Seasonal Autoregressive Integrated Moving Average (SARIMA). In SARIMA model we examine the year to year relationship for each month, since seasonal relationships are between observations for the same month in successive years (Box Jenkins & Reinsel, 1994). The SARIMA model error term ε t is assumed to be serially independent and have zero mean and constant variance (white noise process). 4. State space model with exponential smoothing. The State space model or Dynamic linear model consist of an equation that describes the observed data and some transition equations that describe how the unobserved components or states, like level (l t ), trend (b t ), and seasonality (s t ) change over time. We denote the state space models as ETS for the initials Error, Trend, Seasonal or as ExponenTrial Smoothing (Hyndman and Athanasopoulos, 2012). 4 Forecasting Accuracy Measures Forecast accuracy is assessed using two standard loss functions: the Root Mean Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE) 5

6 Table 2: Equations of Time Series Forecasting Models Forecasting Method/Model Naïve Method ˆx n+h n = x n Seasonal Naïve Method ˆx n+h n = ˆx n+h km Seasonal Autoregressive Integrated Moving Average (SARIMA) φ p (B)Φ P (B s ) d D s x t = c + θ q (B)Θ Q (B s )ε t State space model with exponential smoothing (ETS) Holt-Winters seasonal method with additive errors ˆx t+h t = l t + hb t + s t+h m l t = α(x t s t m + (1 α)(l t 1 + b t 1 )) b t = β (l t l t 1 ) + (1 β )b t 1 s t = γ(x t l t 1 b t 1 + (1 γ)s t m ) Definition n=number of time periods ˆx n+h n =the estimated forecast value x t =the observed car sales at time t n=number of time periods ˆx n+h n =the estimated forecast value h=the forecasting horizon m= is the seasonal period k=[(h-1)/m]+1 x t =dependent variable(car sales at time t), φ p (B)= ordinary autoregressive components order p, B=the backshift operator, θ q (B)= ordinary moving average component ord.q, Φ P (B s )=seasonal autoregressive component ord.p, Θ Q (B s )=moving average components order Q, d = (1 B) d =ordinary difference component, D s = (1 B s ) D =seasonal difference component, d= degree of consecutive differencing, D=degree of seasonal differencing, ε t =error with white noise iidn(0, σ 2 ) l t =estimate of the level of the series at time t b t =estimate of the trend (slope) of the series at time t s t =estimate of the seasonality of the series at time t m=period of seasonality (0 α 1) α= smoothing constant (0 β 1) β =smoothing parameters for trend (0 γ (1 α) γ=smoothing parameters for seasonality 6

7 The RMSE is frequently used for evaluating a model s performance for fitting the data or forecasting them. It calculates the differences between values predicted by a model and the values actually observed. These differences can be the residuals, if the calculation is performed over data sample that was for estimation, or prediction errors if the calculation is in an out-of-sample estimation. The root of the squared sum of these prediction errors divided by the number of time periods results in the RMSE measure. It is usually best to report the RMSE rather than the MSE, because the RMSE is measured in the same units as the data, and not in squared units like MSE, and is therefore representative of the size of a typical error. RMSE is scale-dependent and is not preferred in comparing accuracy across time series with different scales or different variables. However RMSE is a good measure of accuracy to compare forecasted errors of different models for a particular variable. The MAPE evaluation criterion is a great tool for model evaluation and forecasting accuracy because it is not scale-dependent. It is also known as mean absolute percentage deviation and it expresses accuracy as a percentage. The absolute values in the MAPE calculation is summed for every fitted or forecasted point and divided again by the number of fitted points n. Multiplying by 100 makes is a percentage error. MAPE is often preferred because apparently managers understand percentages better than squared errors (Hyndman, Koehler 2006). The only limitations of this measure is in case the data contain zero values (may result in an infinite MAPE) or in case the data contain very small numbers (may result in huge MAPE). However these limitations are of minor importance for this study because our data do not have zero or very small values. Both RMSE and MAPE are calculated for evaluating the out of sample performance of the forecast models. Table 3 illustrate the equations of the accuracy measures used in this study. Table 3: Equation of Error Magnitude Measurements Method/Equation Definition Root Mean Squared Error (RMSE) RMSE = n 1 n (x t f t ) 2 n=number of time periods t=1 x t =the actual number of car sales in period t f t =the forecast value in time period t Mean Absolute Persentage Error (MAPE) MAP E = 100n 1 n t=1 x t f t / x t n=number of time periods x t =the actual number of car sales in period t f t =the forecast value in time period t 5 Empirical Evidence - Conclusions Empirical evidence are given in Table 4. Each one of the four (4) forecasting method is evaluated in two different time periods (A and B) in order to estimate the impact of the economic crisis in sales level. Evidence suggest that the Greek economic crisis had 7

8 influenced the consumption of durable products, like new car sales, as concluded in this study. In time period A ( ) the sample period stops before the recession started. The error measures for this period indicate that a seasonal Naïve model can best capture the fluctuations of sales in the market. That gives evidence of a stable economic activity and an efficient market since the seasonal Naïve model resulted as the best technique in forecasting car sales levels in the Greek retail market. However after the addition of the next 3 years ( ) we have the sample period B, which covers the great recession in Europe and the economic crisis in Greece. During that period all sales level had dramatically fallen and the seasonal Naïve models do not seem to capture the sales level fluctuations any more. In case B, the error magnitude measurements RMSE and MAPE indicate the Holt Winters seasonal model with additive errors as the best model for the out of sample forecast modelling. The ETS models are selected via a state space modelling with exponential smoothing parameters. In our case both data series has an ETS model that has additive errors, with no trend and an additive seasonality which is denoted as an ETS(A,N,A). In other words, both series in this research paper, fit to an exponential smoothing state space model that is equivalent to the Holt-Winters linear model with additive errors (Holt,1957 and Winters, 1960). It is also worth noticing that the Seasonal ARIMA models are the second best choice for forecasting the data in both cases A and B. That shows the quite good and stable way these models fit the data but also indicates that they are not very sensitive in capturing the features or changing movements of the data. In the current turbulent economic situation where customers are reluctant to invest in durable products and buy new cars, there is evidence that exponential smoothing state space models can best forecast the sales level of new cars in the Greek market. However the small sample of this study is not enough to make safe conclusions for all the car representatives operating in the national car market. Therefore this research will be enriched focusing in additional car representatives samples and additional time series forecasting models in order to be completed in the future. Table 4: Evaluations of Forecasting Performances Model RMSE MAPE {Estimation Period}: Forecasting Period Opel Toyota Opel Toyota (1)Naïve Forecasting Method (A){Jan.1998-Dec.2007}:Jan.2008-Dec ,89(4) 1,07(4) 10,78(4) 13,07(4) (B){Jan.1998-Dec.2010}:Jan.2011-Dec ,91(4) 1,24(4) 12,53(4) 17,65(4) (2)Seasonal Naïve Forecasting Method (A){Jan.1998-Dec.2007}:Jan.2008-Dec ,24(1) 0,13(1) 2,40(1) 1,40(1) (B){Jan.1998-Dec.2010}:Jan.2011-Dec ,40(3) 0,71(3) 5,10(3) 8,81(3) (3)SARIMA Forecasting Method (A){Jan.1998-Dec.2007}:Jan.2008-Dec ,26(2) 0,15(2) 2,99(3) 1,83(2) (B){Jan.1998-Dec.2010}:Jan.2011-Dec ,29(2) 0,57(2) 3,61(2) 5,56(2) (4)ETS Forecasting Method (A){Jan.1998-Dec.2007}:Jan.2008-Dec ,24(1) 0,16(3) 2,75(2) 1,90(3) (B){Jan.1998-Dec.2010}:Jan.2011-Dec ,26(1) 0,48(1) 3,22(1) 4,93(1) Note:Figure in parenthesis denote ranking 8

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