Speaker: Dr.Min Wanli

Research Staff Member

Statistical Analysis and Forecasting Group,

Mathematical Science Department,

IBM T. J. Watson Research Center,

Yorktown Heights, NY 10598 USA

Time：2:00 pm, Dec.27(Tuesday)，2005

Location: GSM, Rm.120

Abstract:

In this talk, we consider two aspects of statistical inference on certain time series generated by a sequence of weakly dependent noise, namely, model identification and model selection. Sample (partial) autocorrelation functions play an important role in model identification. The asymptotic behavior of the ACF and PACF of a linear process with iid innovations has been studied extensively. We will consider the same problem for general linear processes with dependent noise such as Threshold AutoRegressive (TAR) and Generalized AutoRegressive Conditional Heteroscadestic (GARCH) processes. Central limit theorems and invariance principles are established under mild conditions within a new framework without mixing conditions. Information criteria are widely used to do model selection in time series analysis. We show the difficulties of existing criteria such as AICc, AIC and BIC in the presence of weakly dependent innovations. We propose a modified criterion and show its efficiency and robustness through simulations.