Second-Order Inference for Nonstationary Time Series

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Han Xiao*+ and Weibiao Wu
• Companies: The University of Chicago and The University of Chicago
• Keywords: nonstationary time series ; locally stationary time series ; time varying covariance function ; auto-covariance matrix ; time varying spectra ; nonparametric estimation

Abstract

We consider the following causal representation of the locally stationary time series $X_i=G(i/n,\mathcal{F}_i)$, where $\mathcal{F}_i=(\epsilon_i,\epsilon_{i-1},\ldots)$ consists of infinitely many independent and identically distributed innovations, and $G:\,\mathbb{R}^\infty \times \mathbb{R} \rightarrow \mathbb{R}$ is a measurable function. We address three problems under this setting. (i) Estimation of the time varying covariance functions and asymptotic distributions of the estimates. (ii) Estimation of the auto-covariance matrices and the consistency in terms of the operator norm. (iii) Estimation of the time varying spectra and their asymptotics.