Article
Full entry |
PDF
(3.3 MB)
Feedback
PDF
(3.3 MB)
Feedback
Keywords:
time series model; asymptotic properties
time series model; asymptotic properties
Summary:
The long memory property of a time series has long been studied and several estimates of the memory or persistence parameter at zero frequency, where the spectral density function is symmetric, are now available. Perhaps the most popular is the log periodogram regression introduced by Geweke and Porter–Hudak [gewe]. In this paper we analyse the asymptotic properties of this estimate in the seasonal or cyclical long memory case allowing for asymmetric spectral poles or zeros. Consistency and asymptotic normality are obtained. Finite sample behaviour is evaluated via a Monte Carlo analysis.
References:
[1] Arteche J.: Gaussian semiparametric estimation in seasonal/cyclical long memory time series. Kybernetika 36 (2000), 279–310 MR 1773505
[2] Arteche J., Robinson P. M.: Seasonal and cyclical long memory. In: Asymptotics, Nonparametrics and Time Series (S. Ghosh ed.), Marcel Dekker, New York 1999, pp. 115–148 MR 1724697 | Zbl 1069.62539
[3] Carlin J. B., Dempster A. P.: Sensitivity analysis of seasonal adjustments: empirical case studies. J. Amer. Statist. Assoc. 84 (1989), 6–20 DOI 10.1080/01621459.1989.10478729 | MR 0999663
[4] Geweke J., Porter–Hudak S.: The estimation and application of long-memory time series models. J. Time Ser. Anal. 4 (1983), 221–238 DOI 10.1111/j.1467-9892.1983.tb00371.x | MR 0738585 | Zbl 0534.62062
[5] Gradshteyn J. S., Ryzhik I. W.: Table of Integrals, Series and Products. Academic Press, Florida 1980 Zbl 1208.65001
[6] Gray H. L., Zhang N. F., Woodward W. A.: On generalized fractional processes. J. Time Ser. Anal. 10 (1989), 233–257 DOI 10.1111/j.1467-9892.1989.tb00026.x | MR 1028940 | Zbl 0685.62075
[7] Hassler U.: Regression of spectral estimators with fractionally integrated time series. J. Time Ser. Anal. 14 (1993), 369–380 DOI 10.1111/j.1467-9892.1993.tb00151.x | MR 1234580 | Zbl 0782.62085
[8] Hassler U.: Corrigendum: The periodogram regression. J. Time Ser. Anal. 14 (1993), 549 DOI 10.1111/j.1467-9892.1993.tb00164.x | MR 1243582
[9] Hassler U.: (Mis)specification of long-memory in seasonal time series. J. Time Ser. Anal. 15 (1994), 19–30 DOI 10.1111/j.1467-9892.1994.tb00174.x | MR 1256854 | Zbl 0794.62059
[10] Hurvich C. M., Beltrao K. I.: Asymptotics for the low frequency ordinates of the periodogram of long memory time series. J. Time Ser. Anal. 14 (1993), 455–472 DOI 10.1111/j.1467-9892.1993.tb00157.x | MR 1243575
[11] Hurvich C. M., Ray B. K.: Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. J. Time Ser. Anal. 16 (1995), 17–42 DOI 10.1111/j.1467-9892.1995.tb00221.x | MR 1323616 | Zbl 0813.62081
[12] Johnson N. L., Kotz S.: Continuous Univariate Distributions – I. Wiley, New York 1970
[13] Jonas A. J.: Persistent Memory Random Processes. Ph.D. Thesis. Department of Statistics, Harvard University, 1983
[14] Loève M.: Probability Theory I. Springer, Berlin 1977 MR 0651017
[15] Ooms M.: Flexible seasonal long-memory and economic time series. Preprint, Erasmus University Rotterdam 1995
[16] Robinson P. M.: Efficient tests of non-stationary hypothesis. J. Amer. Statist. Assoc. 89 (1994), 1420–1437 DOI 10.1080/01621459.1994.10476881 | MR 1310232
[17] Robinson P. M.: Rates of convergence and optimal spectral bandwith for long-range dependence. Probab. Theory Related Fields 99 (1994), 443–473 DOI 10.1007/BF01199901 | MR 1283121
[18] Robinson P. M.: Log-periodogram regression of time series with long-range dependence. Ann. Statist. 23 (1995), 1048–1072 DOI 10.1214/aos/1176324636 | MR 1345214 | Zbl 0838.62085
[20] Velasco C.: Non-stationary log-periodogram regression. J. Econometrics 91 (1999), 325–371 DOI 10.1016/S0304-4076(98)00080-3 | MR 1703950 | Zbl 1041.62533
[21] Zygmund A.: Trigonometric Series. Cambridge University Press, Cambridge U.K. 1977 MR 0617944 | Zbl 1084.42003
Search
Partner of
