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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
    1. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
    2. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    3. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    4. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    5. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    6. Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, pages 177-190.
    7. C. W. J. Granger & Zhuanxin Ding, 1995. "Some Properties of Absolute Return: An Alternative Measure of Risk," Annals of Economics and Statistics, GENES, issue 40, pages 67-91.
    8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, pages 83-106.
    9. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January.
    10. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
    11. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    12. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, pages 782-844.
    13. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, EconWPA.
    14. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    15. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, pages 553-574.
    16. repec:adr:anecst:y:1995:i:40 is not listed on IDEAS
    17. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, pages 104-124.
    18. Barbour, A. D. & Utev, Sergey, 1999. "Compound Poisson approximation in total variation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 89-125, July.
    19. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
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    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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