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An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts

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 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. We analyze the properties of the log periodogram estimate of the memory parameter 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 approximations. We also show the usefulness of our results to distinguish between long memory and level shifts via an application to the volatility of daily returns for wheat commodity futures.

Suggested Citation

  • Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2007-044
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    References listed on IDEAS

    as
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    More about this item

    Keywords

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

    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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