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Pooled Log Periodogram Regression

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Abstract

Estimation of the memory parameter in time series with long range dependence is considered. A pooled log periodogram regression estimator is proposed that utilizes a set of mL periodogram ordinates with L approaching infinity rather than m ordinates used in the conventional log periodogram estimator. Consistency and asymptotic normality of the pooled regression estimator are established. The pooled estimator is shown to have smaller variance but larger bias than the conventional log periodogram estimator. Finite sample performance is assessed in simulations, and the methods are illustrated in an empirical application with inflation and stock returns.

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  • Katsumi Shimotsu & Peter C.B. Phillips, 2000. "Pooled Log Periodogram Regression," Cowles Foundation Discussion Papers 1267, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1267
    Note: CFP 1041
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    1. 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.
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    1. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    2. Caporale, Guglielmo Maria & Gil-Alana, Luis & Plastun, Alex, 2018. "Is market fear persistent? A long-memory analysis," Finance Research Letters, Elsevier, vol. 27(C), pages 140-147.
    3. Cassola, Nuno & Morana, Claudio, 2010. "Comovements in volatility in the euro money market," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 525-539, April.
    4. Morana, Claudio, 2006. "A small scale macroeconometric model for the Euro-12 area," Economic Modelling, Elsevier, vol. 23(3), pages 391-426, May.
    5. Tomasz Wójtowicz & Henryk Gurgul, 2009. "Long memory of volatility measures in time series," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(1), pages 37-54.
    6. Guglielmo Maria Caporale & Luis A. Gil-Alana & Alex Plastun, 2017. "Long Memory and Data Frequency in Financial Markets," Discussion Papers of DIW Berlin 1647, DIW Berlin, German Institute for Economic Research.
    7. Feng, Yuanhua & Beran, Jan, 2008. "Filtered Log-periodogram Regression of long memory processes," CoFE Discussion Papers 08/10, University of Konstanz, Center of Finance and Econometrics (CoFE).
    8. Luis A. Gil-Alana & Antonio Moreno & Seonghoon Cho, 2012. "The Deaton paradox in a long memory context with structural breaks," Applied Economics, Taylor & Francis Journals, vol. 44(25), pages 3309-3322, September.
    9. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    10. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    11. Vides, José Carlos & Golpe, Antonio A. & Iglesias, Jesús, 2021. "The impact of the term spread in US monetary policy from 1870 to 2013," Journal of Policy Modeling, Elsevier, vol. 43(1), pages 230-251.
    12. Henryk Gurgul & Tomasz Wójtowicz, 2006. "Long-run properties of trading volume and volatility of equities listed in DJIA index," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(3-4), pages 29-56.
    13. Morana, Claudio, 2007. "Multivariate modelling of long memory processes with common components," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 919-934, October.
    14. Faÿ, Gilles, 2010. "Moment bounds for non-linear functionals of the periodogram," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 983-1009, June.
    15. Héctor F. Salazar-Núñez & Francisco Venegas-Martínez & Cuauhtémoc Calderón-Villareal, 2017. "¿Existe memoria larga en mercados bursátiles, o depende del modelo, periodo o frecuencia? (Is there Long Memory in Stock Markets, or Does it Depend on the Model, Period or Frequency?)," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 1-24, May.
    16. Omane-Adjepong, Maurice & Alagidede, Paul & Akosah, Nana Kwame, 2019. "Wavelet time-scale persistence analysis of cryptocurrency market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 105-120.
    17. José Carlos Vides & Antonio A. Golpe & Jesús Iglesias, 2018. "How did the Sovereign debt crisis affect the Euro financial integration? A fractional cointegration approach," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 45(4), pages 685-706, November.
    18. Maria Caporale, Guglielmo & Gil-Alana, Luis & Plastun, Alex & Makarenko, Inna, 2013. "Long memory in the ukrainian stock market and financial crises," MPRA Paper 59061, University Library of Munich, Germany.
    19. Dooruj Rambaccussing & Murat Mazibas, 2020. "True versus Spurious Long Memory in Cryptocurrencies," JRFM, MDPI, vol. 13(9), pages 1-11, August.
    20. Henryk GURGUL & Tomasz WÓJTOWICZ, 2006. "Long Memory on the German Stock Exchange," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 56(09-10), pages 447-468, September.
    21. Barros, Carlos Pestana & Gil-Alana, Luis A. & Payne, James E., 2012. "Comovements among U.S. state housing prices: Evidence from fractional cointegration," Economic Modelling, Elsevier, vol. 29(3), pages 936-942.
    22. Bravo Caro, José Manuel & Golpe, Antonio A. & Iglesias, Jesús & Vides, José Carlos, 2020. "A new way of measuring the WTI – Brent spread. Globalization, shock persistence and common trends," Energy Economics, Elsevier, vol. 85(C).
    23. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
    24. Simeon Coleman & Vitor Leone, 2015. "An investigation of regime shifts in UK commercial property returns: a time series analysis," Applied Economics, Taylor & Francis Journals, vol. 47(60), pages 6479-6492, December.
    25. Vides, José Carlos & Golpe, Antonio A. & Iglesias, Jesús, 2020. "The EHTS and the persistence in the spread reconsidered. A fractional cointegration approach," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 124-137.

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    More about this item

    Keywords

    Discrete Fourier transform; log periodogram regression; long memory parameter; pooling frequency bands; semiparametric estimation;
    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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