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An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility

Author

Listed:
  • Pierre Perron

    () (Department of Economics, Boston University)

  • Zhongjun Qu

    () (Department of Economics, Boston University)

Abstract

Recently, 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.

Suggested Citation

  • Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2006-016
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    References listed on IDEAS

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    Cited by:

    1. Carlos Barros & Luis Gil-Alana & Fernando Perez de Gracia, 2016. "Stationarity and Long Range Dependence of Carbon Dioxide Emissions: Evidence for Disaggregated Data," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(1), pages 45-56, January.
    2. David G. McMillan, 2010. "Level-shifts and non-linearity in US financial ratios: Implications for returns predictability and the present value model," Review of Accounting and Finance, Emerald Group Publishing, vol. 9(2), pages 189-207, May.
    3. David E. Rapach & Jack K. Strauss, 2008. "Structural breaks and GARCH models of exchange rate volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 65-90.
    4. McMillan, David G., 2009. "The confusing time-series behaviour of real exchange rates: Are asymmetries important?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(4), pages 692-711, October.
    5. McMillan, David G. & Ruiz, Isabel, 2009. "Volatility persistence, long memory and time-varying unconditional mean: Evidence from 10 equity indices," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(2), pages 578-595, May.

    More about this item

    Keywords

    structural change; jumps; long memory processes; fractional integration; Poisson process; frequency domain estimates.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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