Nonparametric Autoregression and Volatility Estimation

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jin-Hong Park*+
• Companies: College of Charleston
• Keywords: Dimension reduction in Time Series ; Time series central subspace ; Nonlinear time series ; Threshold autoregression ; Autoregressive conditional heteroscedasticity

Abstract

The dimension reduction in regression is an efficient technique of coping with curse of dimensionality in nonparametric regression. Motivated by recent developments for dimension reduction in time series, an empirical application of sufficient dimension reduction to nonparametric autoregression and volatility estimation is shown in this article. Here, we use time series central subspace as a tool for sufficient dimension reduction and estimate it using mutual information index, which is an adaptation of the Kullback-Leibler information. Specifically, we propose an efficient estimation method of minimal dimension and lag using a modified Schwarz Bayesian criterion, when either of the dimension and the lag is unknown. Through simulations and real data analysis, the approach presented in this article performs well in autoregression and volatility estimation in time series.