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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 114 (2003)
Issue (Month): 1 (May)
Pages: 1-27

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Handle: RePEc:eee:econom:v:114:y:2003:i:1:p:1-27

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Velasco, Carlos, . "Non-stationary log-periodogram regression," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4554, Universidad Carlos III de Madrid.
  2. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
  3. Lobato, Ignacio N & Robinson, Peter M, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 475-95, July.
  4. 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(04), pages 686-710, August.
  5. Velasco, Carlos, . "Non-gaussian log-periodogram regression," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3968, Universidad Carlos III de Madrid.
  6. Marc Henry & Peter M Robinson, 1998. "Long and Short Memory Conditional Heteroscedasticity in Estimating the Memory Parameter of Levels - (Now published in Econometric Theory, 15 (1999), pp.299-336.)," STICERD - Econometrics Paper Series /1998/357, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(03), pages 299-336, June.
  8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  9. 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.
  10. Richard Payne & Marc Henry, 1997. "An Investigation of Long Range Dependence in Intra-Day Foreign Exchange Rate Volatility," FMG Discussion Papers dp264, Financial Markets Group.
  11. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
  12. Richard Payne, 1996. "Announcement Effects and Seasonality in the Intra-day Foreign Exchange Market," FMG Discussion Papers dp238, Financial Markets Group.
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Citations

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Cited by:
  1. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  2. 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.
  3. Yixiao Sun & Peter C.B. Phillips, 2002. "Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes," Cowles Foundation Discussion Papers 1366, Cowles Foundation for Research in Economics, Yale University.
  4. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
  5. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2007. "Nonstationarity-extended local Whittle estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1353-1384, December.
  6. Javier Hualde & Peter Robinson, . "Semiparametric Estimation of Fractional Cointegration," Faculty Working Papers 07/06, School of Economics and Business Administration, University of Navarra.
  7. Marc Henry & Paolo Zaffaroni, 2002. "The long range dependence paradigm for macroeconomics and finance," Discussion Papers 0102-19, Columbia University, Department of Economics.
  8. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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