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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

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    15. 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.
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    Citations

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    Cited by:

    1. Chevillon, Guillaume & Mavroeidis, Sophocles, 2017. "Learning can generate long memory," Journal of Econometrics, Elsevier, vol. 198(1), pages 1-9.
    2. Chevillon, Guillaume, 2009. "Multi-step forecasting in emerging economies: An investigation of the South African GDP," International Journal of Forecasting, Elsevier, vol. 25(3), pages 602-628, July.
    3. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
    4. Gabriel Rodríguez & Dennis Alvaro & Ángel Guillén, 2016. " Modelling the Volatility of Commodities Prices using a Stochastic Volatility Model with Random Level Shifts [Modelando la volatilidad de los precios de los commodities utilizando un modelo de volatil," Documentos de Trabajo / Working Papers 2016-414, Departamento de Economía - Pontificia Universidad Católica del Perú.
    5. Rasmus Tangsgaard Varneskov & Pierre Perron, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," CREATES Research Papers 2011-26, Department of Economics and Business Economics, Aarhus University.
    6. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    7. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. " Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    8. Gabriel Rodríguez, 2016. " Modeling Latin-American Stock and Forex Markets Volatility: Empirical Application of a Model with Random Level Shifts and Genuine Long Memory [Modelando la volatilidad de los mercados bursátiles y ca," Documentos de Trabajo / Working Papers 2016-416, Departamento de Economía - Pontificia Universidad Católica del Perú.
    9. Yohei Yamamoto & Pierre Perron, 2013. "Estimating and testing multiple structural changes in linear models using band spectral regressions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 400-429, October.
    10. Peter S. Sephton, 2009. "Fractional integration in agricultural futures price volatilities revisited," Agricultural Economics, International Association of Agricultural Economists, vol. 40(1), pages 103-111, January.
    11. Xu, Jiawen & Perron, Pierre, 2014. "Forecasting return volatility: Level shifts with varying jump probability and mean reversion," International Journal of Forecasting, Elsevier, vol. 30(3), pages 449-463.
    12. Russell Davidson, 2010. "An Agnostic Look at Bayesian Statistics and Econometrics," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 2(2), pages 153-168, June.
    13. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    14. 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.
    15. Andres Herrera & Gabriel Rodríguez, 2014. " Volatility of Stock Market and Exchange Rate Returns in Peru: Long Memory or Short Memory with Level Shifts?," Documentos de Trabajo / Working Papers 2014-393, Departamento de Economía - Pontificia Universidad Católica del Perú.
    16. Chevillon, Guillaume, 2016. "Multistep forecasting in the presence of location shifts," International Journal of Forecasting, Elsevier, vol. 32(1), pages 121-137.
    17. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 399-430, August.
    18. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    19. Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.
    20. repec:eee:ecofin:v:42:y:2017:i:c:p:393-420 is not listed on IDEAS
    21. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, Department of Economics and Business Economics, Aarhus University.

    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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