Higher-Order Kernel Semiparametric M-Estimation of Long Memory
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.
|Date of creation:||Sep 2002|
|Date of revision:|
|Contact details of provider:|| Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
- 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.
- 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.
- 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.
- Donald W.K. Andrews & Patrik Guggenberger, 2000.
"A Bias-Reduced Log-Periodogram Regression Estimator for the Long-Memory Parameter,"
Cowles Foundation Discussion Papers
1263, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- Peter M. Robinson & M. Henry, 1999.
"Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels,"
LSE Research Online Documents on Economics
304, London School of Economics and Political Science, LSE Library.
- 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.
- Peter M. Robinson & Marc Henry, 1998. "Long and short memory conditional heteroscedasticity in estimating the memory parameter of levels," LSE Research Online Documents on Economics 2022, London School of Economics and Political Science, LSE Library.
- 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.
- Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
- Josu Arteche & Peter M. Robinson, 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
- 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.
- 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.
- Richard Payne, 1996. "Announcement Effects and Seasonality in the Intra-day Foreign Exchange Market," FMG Discussion Papers dp238, Financial Markets Group.
When requesting a correction, please mention this item's handle: RePEc:cep:stiecm:/2002/436. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.