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 InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 28 (2010)
Issue (Month): 2 ()
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Other versions of this item:
- Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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