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Higher-order kernel semiparametric M-estimation of long memory

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  • Robinson, Peter M.
  • Henry, Marc

Abstract

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We introduce a broad class of such semiparametric estimates that also covers pooling across frequencies. A leading "Box-Club" sub-class, indexed by a single tuning parameter, interpolates between the popular local log periodogram and local Whittle estimates, leading to a smooth interpolation of asymptotic variances. The bias of these two estimates also differs to higher order, and we also show how bias, and asymptotic mean square error, can be reduced, across the class of estimates studied, by means of a suitable version of higher-order kernels. We thence calculate an optimal bandwidth (the number of low frequency periodogram ordinates employed) which minimizes this mean squared error. Finite sample performance is studied in a small Monte Carlo experiment, and an empirical application to intra-day foreign exchange returns is included.
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  • Robinson, Peter M. & Henry, Marc, 2003. "Higher-order kernel semiparametric M-estimation of long memory," Journal of Econometrics, Elsevier, vol. 114(1), pages 1-27, May.
  • Handle: RePEc:eee:econom:v:114:y:2003:i:1:p:1-27
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    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. 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(4), pages 686-710, August.
    12. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    13. Donald W.K. Andrews & Yixiao Sun, 2001. "Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1293, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    2. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series 502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    4. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    5. Hualde, Javier & Robinson, Peter M., 2006. "Semiparametric Estimation of Fractional Cointegration," LSE Research Online Documents on Economics 4537, London School of Economics and Political Science, LSE Library.
    6. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    7. Ye, Xunyu & Gao, Ping & Li, Handong, 2015. "Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram," Economic Modelling, Elsevier, vol. 46(C), pages 167-179.
    8. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.
    9. 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.
    10. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
    11. García-Enríquez, Javier & Hualde, Javier, 2019. "Local Whittle estimation of long memory: Standard versus bias-reducing techniques," Econometrics and Statistics, Elsevier, vol. 12(C), pages 66-77.

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    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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