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Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration

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  • Morten Ørregaard Nielsen
  • Per Houmann Frederiksen

Abstract

In this paper we compare through Monte Carlo simulations the finite sample properties of estimators of the fractional differencing parameter, d. This involves frequency domain, time domain, and wavelet based approaches, and we consider both parametric and semiparametric estimation methods. The estimators are briefly introduced and compared, and the criteria adopted for measuring finite sample performance are bias and root mean squared error. Most importantly, the simulations reveal that (1) the frequency domain maximum likelihood procedure is superior to the time domain parametric methods, (2) all the estimators are fairly robust to conditionally heteroscedastic errors, (3) the local polynomial Whittle and bias-reduced log-periodogram regression estimators are shown to be more robust to short-run dynamics than other semiparametric (frequency domain and wavelet) estimators and in some cases even outperform the time domain parametric methods, and (4) without sufficient trimming of scales the wavelet-based estimators are heavily biased.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:emetrv:v:24:y:2005:i:4:p:405-443
    DOI: 10.1080/07474930500405790
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    Cited by:

    1. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    2. Marcel Aloy & Gilles Truchis, 2016. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems and the Co-persistence Analysis of Stock Market Realized Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 83-104, June.
    3. Hiremath, Gourishankar S & Bandi, Kamaiah, 2011. "Testing Long Memory in Stock Returns of Emerging Markets: Some Further Evidence," MPRA Paper 48517, University Library of Munich, Germany.
    4. 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.
    5. Morana, Claudio, 2006. "A small scale macroeconometric model for the Euro-12 area," Economic Modelling, Elsevier, vol. 23(3), pages 391-426, May.
    6. Afonso Goncalves da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 268-297.
    7. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    8. Baillie Richard T. & Kapetanios George, 2016. "On the estimation of short memory components in long memory time series models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 365-375, September.
    9. K. Nadarajah & Gael M. Martin & D.S. Poskitt, 2014. "Issues in the Estimation of Mis-Specified Models of Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers 18/14, Monash University, Department of Econometrics and Business Statistics.
    10. Orlov, Vitaly & Äijö, Janne, 2015. "Benefits of wavelet-based carry trade diversification," Research in International Business and Finance, Elsevier, vol. 34(C), pages 17-32.
    11. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.
    12. Kraicová Lucie & Baruník Jozef, 2017. "Estimation of long memory in volatility using wavelets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    13. Grassi, Stefano & Santucci de Magistris, Paolo, 2014. "When long memory meets the Kalman filter: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 301-319.
    14. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.
    15. Aloy Marcel & Tong Charles Lai & Peguin-Feissolle Anne & Dufrénot Gilles, 2013. "A smooth transition long-memory model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 281-296, May.
    16. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
    17. Marcel Aloy & Gilles De Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
    18. Yushu Li, 2015. "Estimate Long Memory Causality Relationship by Wavelet Method," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 531-544, April.
    19. Sophie Achard & Irène Gannaz, 2016. "Multivariate Wavelet Whittle Estimation in Long-range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 476-512, July.
    20. 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.
    21. Aaron Smallwood; Alex Maynard; Mark Wohar, 2005. "The Long and the Short of It: Long Memory Regressors and Predictive Regressions," Computing in Economics and Finance 2005 384, Society for Computational Economics.

    More about this item

    Keywords

    Bias; Finite sample distribution; Fractional integration; Maximum likelihood; Monte Carlo simulation; Parametric estimation; Semiparametric estimation; Wavelet;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation 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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