Inference for Local Autocorrelation Process in Locally Stationary Models

• Activity Number: 327
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Zhibiao Zhao*+
• Companies: Penn State University
• Keywords: Local autocorrelation ; Locally stationary model ; Nonparametric regression ; Simultaneous confidence band ; Testing for zero autocorrelation ; Time series

Abstract

For nonstationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. For locally stationary models, we construct a simultaneous confidence band for their local autocorrelation process with asymptotically correct coverage probabilities. The simultaneous confidence band can be used to address hypothesis testing problems by examining whether a parametric autocorrelation curve is entirely contained within the band. In particular, we investigate two important problems: testing whether the local autocorrelation process is indeed time-varying, and testing whether the local autocorrelation is zero. Simulation studies and two empirical applications are developed. For the global temperature series, we find that the local autocorrelations are time-varying and have a "V" shape during 1910-1960. For the S&P 500 index, we conclude that the returns satisfy the efficient-market hypothesis whereas the magnitudes of returns show significant local autocorrelations.