Log-periodogram regression in asymmetric long memory

Josu Arteche

Kybernetika (2000)

  • Volume: 36, Issue: 4, page [415]-435
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Arteche, Josu. "Log-periodogram regression in asymmetric long memory." Kybernetika 36.4 (2000): [415]-435. <http://eudml.org/doc/33493>.

@article{Arteche2000,
abstract = {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.},
author = {Arteche, Josu},
journal = {Kybernetika},
keywords = {time series model; asymptotic properties; time series; asymptotic properties},
language = {eng},
number = {4},
pages = {[415]-435},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Log-periodogram regression in asymmetric long memory},
url = {http://eudml.org/doc/33493},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Arteche, Josu
TI - Log-periodogram regression in asymmetric long memory
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 4
SP - [415]
EP - 435
AB - 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.
LA - eng
KW - time series model; asymptotic properties; time series; asymptotic properties
UR - http://eudml.org/doc/33493
ER -

References

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  1. Arteche J., Gaussian semiparametric estimation in seasonal/cyclical long memory time series, Kybernetika 36 (2000), 279–310 MR1773505
  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 (1999) Zbl1069.62539MR1724697
  3. Carlin J. B., Dempster A. P., 10.1080/01621459.1989.10478729, J. Amer. Statist. Assoc. 84 (1989), 6–20 (1989) MR0999663DOI10.1080/01621459.1989.10478729
  4. Geweke J., Porter–Hudak S., 10.1111/j.1467-9892.1983.tb00371.x, J. Time Ser. Anal. 4 (1983), 221–238 (1983) Zbl0534.62062MR0738585DOI10.1111/j.1467-9892.1983.tb00371.x
  5. Gradshteyn J. S., Ryzhik I. W., Table of Integrals, Series and Products, Academic Press, Florida 1980 Zbl1208.65001
  6. Gray H. L., Zhang N. F., Woodward W. A., 10.1111/j.1467-9892.1989.tb00026.x, J. Time Ser. Anal. 10 (1989), 233–257 (1989) Zbl0685.62075MR1028940DOI10.1111/j.1467-9892.1989.tb00026.x
  7. Hassler U., 10.1111/j.1467-9892.1993.tb00151.x, J. Time Ser. Anal. 14 (1993), 369–380 (1993) Zbl0782.62085MR1234580DOI10.1111/j.1467-9892.1993.tb00151.x
  8. Hassler U., 10.1111/j.1467-9892.1993.tb00164.x, J. Time Ser. Anal. 14 (1993), 549 (1993) MR1243582DOI10.1111/j.1467-9892.1993.tb00164.x
  9. Hassler U., 10.1111/j.1467-9892.1994.tb00174.x, J. Time Ser. Anal. 15 (1994), 19–30 (1994) Zbl0794.62059MR1256854DOI10.1111/j.1467-9892.1994.tb00174.x
  10. Hurvich C. M., Beltrao K. I., 10.1111/j.1467-9892.1993.tb00157.x, J. Time Ser. Anal. 14 (1993), 455–472 (1993) MR1243575DOI10.1111/j.1467-9892.1993.tb00157.x
  11. Hurvich C. M., Ray B. K., 10.1111/j.1467-9892.1995.tb00221.x, J. Time Ser. Anal. 16 (1995), 17–42 (1995) Zbl0813.62081MR1323616DOI10.1111/j.1467-9892.1995.tb00221.x
  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 MR0651017
  15. Ooms M., Flexible seasonal long-memory and economic time series, Preprint, Erasmus University Rotterdam 1995 
  16. Robinson P. M., 10.1080/01621459.1994.10476881, J. Amer. Statist. Assoc. 89 (1994), 1420–1437 (1994) MR1310232DOI10.1080/01621459.1994.10476881
  17. Robinson P. M., 10.1007/BF01199901, Probab. Theory Related Fields 99 (1994), 443–473 (1994) MR1283121DOI10.1007/BF01199901
  18. Robinson P. M., 10.1214/aos/1176324636, Ann. Statist. 23 (1995), 1048–1072 (1995) Zbl0838.62085MR1345214DOI10.1214/aos/1176324636
  19. Velasco C., 10.1016/S0304-4076(98)00080-3, J. Econometrics 91 (1999), 325–371 (1999) Zbl1041.62533MR1703950DOI10.1016/S0304-4076(98)00080-3
  20. Zygmund A., Trigonometric Series, Cambridge University Press, Cambridge U.K. 1977 Zbl1084.42003MR0617944

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