Investigation of periodicity for dependent observations

Tomáš Cipra

Aplikace matematiky (1984)

  • Volume: 29, Issue: 2, page 134-142
  • ISSN: 0862-7940

Abstract

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It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.

How to cite

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Cipra, Tomáš. "Investigation of periodicity for dependent observations." Aplikace matematiky 29.2 (1984): 134-142. <http://eudml.org/doc/15340>.

@article{Cipra1984,
abstract = {It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.},
author = {Cipra, Tomáš},
journal = {Aplikace matematiky},
keywords = {test for periodicity; time series; dependent observations; test for periodicity; time series; dependent observations},
language = {eng},
number = {2},
pages = {134-142},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Investigation of periodicity for dependent observations},
url = {http://eudml.org/doc/15340},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Cipra, Tomáš
TI - Investigation of periodicity for dependent observations
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 2
SP - 134
EP - 142
AB - It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.
LA - eng
KW - test for periodicity; time series; dependent observations; test for periodicity; time series; dependent observations
UR - http://eudml.org/doc/15340
ER -

References

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  1. J. Anděl, Statistical Analysis of Time Series, SNTL, Prague, 1976 (in Czech). (1976) 
  2. E. Bølviken, New tests of significance in periodogram analysis, Scand. J. Statist. 10 (1983), 1-10. (1983) MR0711329
  3. T. Cipra, Improvement of Fisher's test of periodicity, Apl. mat. 28 (1983), 186- 193. (1983) Zbl0528.62075
  4. E. Damsleth E. Spjøtvoll, 10.1080/01621459.1982.10477820, Journal of the American Statistical Association 77 (1982), 381- 387. (1982) DOI10.1080/01621459.1982.10477820
  5. R. A. Fisher, Tests of significance in harmonic analysis, Proc. Roy. Soc. A 125 (1929), 54-59. (1929) 
  6. R. A. Fisher, 10.1111/j.1469-1809.1939.tb02211.x, Annals of Eugenics 9 (1939), 238-249. (1939) MR0001499DOI10.1111/j.1469-1809.1939.tb02211.x
  7. R. A. Fisher, 10.1111/j.1469-1809.1940.tb02233.x, Annals of Eugenics 10 (1940), 14-17. (1940) MR0002079DOI10.1111/j.1469-1809.1940.tb02233.x
  8. E. J. Hannan, Time Series Analysis, Methuen, London, 1960. (1960) Zbl0095.13204MR0114281
  9. E. J. Hannan, Testing for a jump in the spectral function, J. R. Statist. Soc. B 23 (1961), 394-404. (1961) Zbl0109.12801MR0137271
  10. J. B. Mac Neill, 10.1093/biomet/61.1.57, Biometrika 61 (1974), 57-70. (1974) MR0378317DOI10.1093/biomet/61.1.57
  11. D. F. Nicholls, 10.1111/j.1467-842X.1967.tb00188.x, Aust. J. Statist. 9 (1967), 103-108. (1967) MR0228133DOI10.1111/j.1467-842X.1967.tb00188.x
  12. M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London-New York, 1981. (1981) Zbl0537.62075
  13. A. F. Siegel, 10.1093/biomet/66.2.381, Biometrika 66 (1979), 381-386. (1979) MR0548209DOI10.1093/biomet/66.2.381
  14. A. F. Siegel, 10.1080/01621459.1980.10477474, Journal of the American Statistical Association 75 (1980), 345-348. (1980) Zbl0462.62069DOI10.1080/01621459.1980.10477474
  15. A. M. Walker, 10.1017/S1446788700025921, J. Aust. Math. Soc. 5 (1965), 107-128. (1965) Zbl0128.38701MR0177457DOI10.1017/S1446788700025921
  16. P. Whittle, Hypothesis Testing in Time Series Analysis, Almqvist and Wiksell, Uppsala, 1951. (1951) Zbl0045.41301MR0040634
  17. P. Whittle, 10.1093/biomet/39.3-4.309, Biometrika 39 (1952), 309-318. (1952) MR0052743DOI10.1093/biomet/39.3-4.309
  18. P. Whittle, The statistical analysis of a seiche record, Sears Foundation Journal of Marine Research 13 (1954), 76-100. (1954) MR0078600

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