Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices
AbstractRecently, there has been an upsurge of interest in the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from zero and the autocovariance function exhibits a slow rate of decay, akin to a long memory process. Partly based on results in Perron and Qu (2007), we analyze the properties of the autocorrelation function, the periodogram and the log periodogram estimate of the memory parameter when the level shift component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. We confront our theoretical predictions using log-squared returns as a proxy for the volatility of some assets returns, including daily S&P 500 returns over the period 1928-2002. The autocorrelations and the path of the log periodogram estimates follow patterns that would obtain if the true underlying process was one of short-memory contaminated by level shifts instead of a fractionally integrated process. A simple testing procedure is also proposed, which reinforces this conclusion.
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Bibliographic InfoPaper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2008-004.
Date of creation: Aug 2008
Date of revision:
structural change; jumps; long memory processes; fractional integration; frequency domain estimates;
Other versions of this item:
- Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-10 (All new papers)
- NEP-ECM-2009-06-10 (Econometrics)
- NEP-ETS-2009-06-10 (Econometric Time Series)
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