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

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Author Info
Pierre Perron () (Department of Economics, Boston University,)
Zhongjun Qu () (Department of Economics, Boston University,)

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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.

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Publisher Info
Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2007-044.

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Length: 32
Date of creation: Oct 2007
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Handle: RePEc:bos:wpaper:wp2007-044

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Related research
Keywords: 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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July. [Downloadable!] (restricted)
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  2. Leipus, Remigijus & Viano, Marie-Claude, 2003. "Long memory and stochastic trend," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 177-190, January. [Downloadable!] (restricted)
  3. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November. [Downloadable!] (restricted)
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  4. 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, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  5. I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996. [Downloadable!]
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  6. Gourieroux, Christian & Jasiak, Joann, 2001. "Memory and infrequent breaks," Economics Letters, Elsevier, vol. 70(1), pages 29-41, January. [Downloadable!] (restricted)
  7. 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. [Downloadable!]
  8. Iliyan GEORGIEV, 2002. "Functional Weak Limit Theory for Rare Outlying Events," Economics Working Papers ECO2002/22, European University Institute. [Downloadable!]
  9. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation, Yale University. [Downloadable!]
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  10. 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. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
  12. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  13. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November. [Downloadable!] (restricted)
  14. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Zhongjun Qu & Pierre Perron, 2008. "A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and NASDAQ Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-007, Boston University - Department of Economics. [Downloadable!]
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