by Marco Hülsmann, Christoph M. Friedrich and Dirk Reith

The Fraunhofer-Institute for Algorithms and Scientific Computing (SCAI) has developed a software tool for sales forecasts using a methodology that consists of a combination of time series analysis and data mining techniques.

Successful corporate management depends on efficient strategic and operative planning. In this context, reliable forecasts make an important contribution. As the automobile industry is one of the most important sectors of the German economy, its development is of the utmost interest. Developments in both mathematical algorithms and computing power have increased the reliability of forecasts enormously. Enhanced methods such as data mining, and advanced technology allowing the storage and evaluation of large empirical data sets, mean that forecasts are more reliable than ever before. At the same time, the explicability of a forecast model is as important as its reliability. In cooperation with the service company BDW Automotive, which consists of market experts in the automobile industry, the Fraunhofer-Institute for Algorithms and Scientific Computing (SCAI) has developed a software tool for sales forecasts, wherein the methods applied are highly accurate and at the same time easily explicable.

The data for this model consists largely of registrations of new automobiles as well as economic exogenous parameters like the Gross Domestic Product, the Consumer Price Index, the Unemployment Rate, the Interest Rate and the Industrial Investment Demand: these are available from the Federal Statistical Office and the German Federal Bank, mostly as monthly or quarterly data. In addition, market experts provide domain-specific economic factors like Latent Replacement Demand and Model Policy. Our software tool is able to generate forecasts for monthly, quarterly and yearly time intervals; if the data is not published at the required time interval, conversions are performed. As the German automobile market increased extraordinarily due to the reunification of the two German states in 1990, this could only be treated as a massive shock event, which caused all data prior to 1992 to be discarded. We therefore used yearly, monthly and quarterly data from 1992 to 2008 for our software tool. This has led to a model based on the past that is considered capable of making reliable predictions for the future.

The methodology consists of a combination of time series analysis and data mining techniques. New car registrations are considered as a time series composed additively of trend, seasonal and calendar components, which are assumed to be independent. The seasonal and calendar components are estimated by standard time-series analysis methods, whereas the trend component is multivariate, ie it depends on economic exogenous parameters and is therefore estimated by data mining techniques. The simplest method applied in this context was multivariate linear regression. However, it delivered poor results, as the trend could not be assumed to be roughly linear. Hence, nonlinear trend estimators were used, which yielded much more reliable results, eg a Support Vector Machine with a Gaussian kernel, Decision Trees, K-Nearest-Neighbour and Random Forest.

Model Evaluation and Limitation of Forecasts
In order to evaluate the model, a training period and an adjacent test period must be defined. In the former, the model is built by estimating trend, seasonal and calendar components, and for the latter, a forecast is made, with the predicted registrations of automobiles being compared to real data. Taking the period from 1992 to 2006 as the training period and 2007/2008 as the testing period, the average error on the predicted registrations is very low (0.1-1% for yearly, 4-6% for quarterly and 6-7% for monthly data) using high-performance nonlinear data mining techniques. These low error rates represent a very good performance of our forecast tool.

Due to the expertise of BDW Automotive, external perturbations can be taken into consideration. For example, the rise in the German sales tax in 2007 from 16% to 19% led to increased sales in 2006, and the recent financial crisis led to a decrease in the last two quarters of 2008. It should be pointed out that forecasts are always limited by uncertainties caused by perturbations in the future, which are not predictable or whose effects cannot be assessed. The current grant of the scrapping bonus in Germany, which led to higher sales in the year 2009, is another such occurrence. As a result, reliable trend forecasts can always be achieved but more detailed forecasts must be interpreted with care, as they cannot handle random events.

Future Work
The focus now lies on applying our software tool to other traditional major markets, eg France, Japan and the USA. This will require different exogenous parameters to be considered along with different economic perturbations.

Please contact:
Dirk Reith
Fraunhofer-Institute for Algorithms and Scientific Computing (SCAI), Germany
Tel: +49 2241 142746

Next issue: January 2021
Special theme:
"Epidemic Modelling"
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