Implementation Of Bootstrap Techniques For Econometric Forecasts: Illustrations In The Car Industry

Bootstrap techniques, which were developed from the original work of Efron (1979), lead to interesting results on regression models (Freedman, 1981), when information on the distribution of disturbance terms are not available. Stine (1985) carried out the implementation of these techniques on forecasting, in order to build prediction intervals. Such developments were particularly useful for the prediction of industrial costs when samples are small and distribution of the error term is unknown. This concerned particularly econometric cost models in car industry. The implementation of such methods is time consuming (large number of bootstrap replications) and had to be improved for operational perspectives. Thus, some ways of computation, which strongly reduced required computing power, were imagined. First, an ordinary least square estimator based on the pseudo-inverse of the explanatory variables matrix (Belsey, Kuh and Welsch, 1980) was used instead of a traditional matrix reversed by Cholesky decomposition. Such calculations ran faster on small size samples (comparisons were made both on PC and SUN working station). Second, a modified sorting technique for empirical bootstrap replications was proposed. Only distribution tails were sorted and each element of the series was compared to the retained percentiles, which stood as the lower and upper bound of the confidence interval. Thus, the distribution between these percentiles was not sorted, which is not useful for our purpose. Finally, a strategy based on the median and the coefficient of variation to determine the required number of bootstrap replications was explored. Our applications dealt with cost forecasting in car industry. Such predictions were made during the first stage of an automotive project, i.e. three years before the production launching of the new car. The available information were cross-section data on current vehicles which obviously induced small samples. Moreover, the error term had not necessarily a Gaussian distribution. Consequently, the use of bootstrap techniques strongly improved prediction intervals by reflecting the original distribution of the data through the empirical one.