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Log-periodogram estimation of the memory parameter of a long-memory process under trend

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  • Sibbertsen, Philipp

Abstract

We show that log-periodogram-based estimators for the memory parameter in a stationary invertible long-memory process do not confuse small trends with long-range dependence. In the case of slowly decaying trends we show by Monte Carlo methods that the tapered periodogram is quite robust against these trends and reduces the bias obtained when employing the standard log-periodogram estimator. Thus, comparing the tapered and the non-tapered estimator gives a tool at hand for distinguishing slowly decaying trends and long-range dependence.

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  • Sibbertsen, Philipp, 2003. "Log-periodogram estimation of the memory parameter of a long-memory process under trend," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 261-268, February.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:3:p:261-268
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    1. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    2. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    4. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    5. C. C. Heyde & W. Dai, 1996. "On The Robustness To Small Trends Of Estimation Based On The Smoothed Periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(2), pages 141-150, March.
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    1. repec:ebl:ecbull:v:7:y:2003:i:3:p:1-13 is not listed on IDEAS
    2. Jussi Tolvi, 2003. "Long memory in a small stock market," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-13.
    3. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    4. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    5. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2010. "Long memory volatility in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1425-1433.
    6. Philipp Sibbertsen, 2004. "Long memory in volatilities of German stock returns," Empirical Economics, Springer, vol. 29(3), pages 477-488, September.
    7. Sibbertsen, Philipp & Venetis, Ioannis, 2003. "Distinguishing between long-range dependence and deterministic trends," Technical Reports 2003,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Canarella, Giorgio & Miller, Stephen M., 2017. "Inflation targeting and inflation persistence: New evidence from fractional integration and cointegration," Journal of Economics and Business, Elsevier, vol. 92(C), pages 45-62.

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    More about this item

    Keywords

    Long memory Trends Log-periodogram regression;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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