Analysing nonlinear time series with central subspace

Abstract

Traditionally, time series analysis involves building an appropriate model and using either parametric or nonparametric methods to make inference about the model parameters. Motivated by recent developments for dimension reduction in time series, an empirical application of sufficient dimension reduction (SDR) to nonlinear time series modelling is shown in this article. Here, we use time series central subspace as a tool for SDR and estimate it using mutual information index. Especially, in order to reduce the computational complexity in time series, we propose an efficient estimation method of minimal dimension and lag using a modified Schwarz–Bayesian criterion, when either of the dimensions and the lags is unknown. Through simulations and real data analysis, the approach presented in this article performs well in autoregression and volatility estimation.

Keywords:

• nonlinear time series
• sufficient dimension reduction
• time series central subspace
• threshold autoregression
• autoregressive conditional heteroscedasticity

Acknowledgements

The author wishes to thank a referee for the constructive comments that improved the presentation of this article. This work is supported in part by the Research and Development of Mathematics Department at the College of Charleston.