A Nonlinear Model of Economic Data Related to the German Automobile Industry

Prediction of economic variables is a basic component not only for economic models, but also for many business decisions. But it is difficult to produce accurate predictions in times of economic crises, which cause nonlinear effects in the data. Such evidence appeared in the German automobile industry as a consequence of the financial crisis in 2008/09, which influenced exchange rates and automobile manufacturers’ share prices. In this essay a new method of time series analysis, Autoregressive Neural Network Vector Error Correction Models (ARNN-VECM), based on the concept of nonlinear cointegration of Escribano and Mira [1] and the universal approximation property of single hidden layer feedforward neural networks of Hornik [2] is used for prediction and analysis of the relationships between 4 variables related to the German automobile industry: The US Dollar to Euro exchange rate, the industrial production of the German automobile industry, the sales of imported cars in the USA and an index of shares of German automobile manufacturing companies. The model differentiates between two kinds of relationships: The long run linear relationship (the cointegration relationship) is estimated with a 2SLS method, whereas the stock index is used as instrumental variable. This is due to the fact that share prices are an incentive for management to optimize its operating business. The short run adjustment is the nonlinear part of the model, in which the long run relationship is adjusted at nonlinear temporal occurrence. This part of the model improves the prediction power of the ARNN-VECM significantly, as it is able to handle the crisis of 2008/09. Monthly data from January 1999 to September 2009 are used for estimation of the models. They are estimated using several testing and inference methods for optimal model design as well as a customized Levenberg-Marquardt algorithm for optimization of the parameters. Prediction results are compared to various linear and nonlinear univariate and multivariate models, which are all outperformed by the ARNN VECM concerning short run prediction. Keywords Nonlinear Time Series Analysis, Vector Error Correction, Neural Networks, Financial Crisis, German Automobile Industry.