Boosting Techniques for Nonlinear Time Series Models

Many of the popular nonlinear time series models require a priori the choice of parametric functions which are assumed to be appropriate in specific applications. This approach is used mainly in financial applications, when sufficient knowledge is available about the nonlinear structure between the covariates and the response. One principal strategy to investigate a broader class on nonlinear time series is the Nonlinear Additive AutoRegressive (NAAR) model. The NAAR model estimates the lags of a time series as flexible functions in order to detect nonmonotone relationships between current observations and past values. We consider linear and additive models for identifying nonlinear relationships. A componentwise boosting algorithm is applied to simultaneous model fitting, variable selection, and model choice. Thus, with the application of boosting for fitting potentially nonlinear models we address the major issues in time series modelling: lag selection and nonlinearity. By means of simulation we compare the outcomes of boosting to the outcomes obtained through alternative nonparametric methods. Boosting shows an overall strong performance in terms of precise estimations of highly nonlinear lag functions. The forecasting potential of boosting is examined on real data where the target variable is the German industrial production (IP). In order to improve the model’s forecasting quality we include additional exogenous variables. Thus we address the second major aspect in this paper which concerns the issue of high-dimensionality in models. Allowing additional inputs in the model extends the NAAR model to an even broader class of models, namely the NAARX model. We show that boosting can cope with large models which have many covariates compared to the number of observations. keywords: componentwise boosting, forecasting, nonlinear times series, autoregressive additive models, lag selection. ∗Corresponding author. Email: [email protected], Tel.: +49 89 2180 6407, Fax: +49 89 2180 5040