Inference for Local Autocorrelations in Locally Stationary Models

• Published in: Journal of business & economic statistics Vol. 33; no. 2; pp. 296 - 306
• Main Author: Zhao, Zhibiao
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 03.04.2015; American Statistical Association; Taylor & Francis Ltd
• Subjects: Correlation analysis; Efficient markets; Hypotheses; Hypothesis testing; Mathematical models; Nonparametric regression; Normal distribution; Simulation; Simultaneous confidence band; Statistical inference; Studies; Testing for zero autocorrelation; Time series; Locally stationary model; Simultaneous confidence band; Testing for zero autocorrelation; Nonparametric regression; Time series; Local autocorrelation
• ISSN: 0735-0015; 1537-2707
• DOI: 10.1080/07350015.2014.948177

For nonstationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our result provides an important generalization of the R function acf() to locally stationary Gaussian processes. 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.