Boosting techniques for nonlinear time series models

摘要

Many of the popular nonlinear time series models require a priori the choice of parametric functions which are assumed to be appropriate in specific ap plications. This approach is mainly used 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 se ries is the Nonlinear Additive AutoRegressive (NAAR) model. The NAAR model es timates the lags of a time series as flexible functions in order to detect non-monotone relationships between current and past observations. We consider linear and additive models for identifying nonlinear relationships. A componentwise boosting algorithm is applied for 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 boosting to alternative nonparametric methods. Boosting shows a strong overall performance in terms of precise estimations of highly nonlin ear lag functions. The forecasting potential of boosting is examined on the German industrial production (IP); to improve the model's forecasting quality we include ad ditional exogenous variables. Thus we address the second major aspect in this paper which concerns the issue of high dimensionality in models. Allowing additional in puts in the model extends the NAAR model to a 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.