An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility
AbstractRecently, there has been an upsurge of interest on the possibility of confusing long memory and structural changes in level. Many studies have documented the fact 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. Yet, no theoretical results are available pertaining to the distributions of the estimates. We fill this gap by analyzing the properties of the log periodogram estimate when the jump component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. Simulations are presented to highlight the properties of the distributions and to assess the adequacy of our limit results as approximations to the finite sample distributions. Also, we explain how the limit distribution changes as the number of frequencies used varies, a feature that is different from the case with a pure fractionally integrated model. We confront this practical implication to daily SP500 absolute returns and their square roots over the period 1928-2002. Our findings are remarkable, the path of the log periodogram estimates clearly follows a pattern that would obtain if the true underlying process was one of short-memory contaminated by level shifts instead of a pure 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 WP2006-016.
Date of creation: Dec 2006
Date of revision:
structural change; jumps; long memory processes; fractional integration; Poisson process; frequency domain estimates.;
Find related papers by JEL classification:
- 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-2007-08-14 (All new papers)
- NEP-ECM-2007-08-14 (Econometrics)
- NEP-ETS-2007-08-14 (Econometric Time Series)
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