Geodesic
Investigation of periodicity for dependent observations
Applications of Mathematics, Tome 29 (1984) no. 2, pp. 134-142
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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.
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.
DOI : 10.21136/AM.1984.104076
Classification : 62M02, 62M07, 62M10, 62M15
Keywords: test for periodicity; time series; dependent observations 
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Cipra, Tomáš. Investigation of periodicity for dependent observations. Applications of Mathematics, Tome 29 (1984) no. 2, pp. 134-142. doi: 10.21136/AM.1984.104076

[1] J. Anděl: Statistical Analysis of Time Series. SNTL, Prague, 1976 (in Czech).

[2] E. Bølviken: New tests of significance in periodogram analysis. Scand. J. Statist. 10 (1983), 1-10. | MR

[3] T. Cipra: Improvement of Fisher's test of periodicity. Apl. mat. 28 (1983), 186- 193. | Zbl

[4] E. Damsleth E. Spjøtvoll: Estimation of trigonometric component in times series. Journal of the American Statistical Association 77 (1982), 381- 387. | DOI

[5] R. A. Fisher: Tests of significance in harmonic analysis. Proc. Roy. Soc. A 125 (1929), 54-59.

[6] R. A. Fisher: The sampling distribution of some statistics obtained from non-linear equations. Annals of Eugenics 9 (1939), 238-249. | DOI | MR

[7] R. A. Fisher: On the similarity of the distribution found for the test of significance in harmonic analysis and in Steven's problem in geometrical probability. Annals of Eugenics 10 (1940), 14-17. | DOI | MR

[8] E. J. Hannan: Time Series Analysis. Methuen, London, 1960. | MR | Zbl

[9] E. J. Hannan: Testing for a jump in the spectral function. J. R. Statist. Soc. B 23 (1961), 394-404. | MR | Zbl

[10] J. B. Mac Neill: Tests for periodic components in multiple time series. Biometrika 61 (1974), 57-70. | DOI | MR

[11] D. F. Nicholls: Estimation of the spectral density function when testing for a jump in the spectrum. Aust. J. Statist. 9 (1967), 103-108. | DOI | MR

[12] M. B. Priestley: Spectral Analysis and Time Series. Academic Press, London-New York, 1981. | Zbl

[13] A. F. Siegel: The noncentral chi squared distribution with zero degree of freedom and testing for uniformity. Biometrika 66 (1979), 381-386. | DOI | MR

[14] A. F. Siegel: Testing for periodicity in a time series. Journal of the American Statistical Association 75 (1980), 345-348. | DOI | Zbl

[15] A. M. Walker: Some asymptotic results for the periodogram of a stationary time series. J. Aust. Math. Soc. 5 (1965), 107-128. | DOI | MR | Zbl

[16] P. Whittle: Hypothesis Testing in Time Series Analysis. Almqvist and Wiksell, Uppsala, 1951. | MR | Zbl

[17] P. Whittle: Test of fit in time series. Biometrika 39 (1952), 309-318. | DOI | MR

[18] P. Whittle: The statistical analysis of a seiche record. Sears Foundation Journal of Marine Research 13 (1954), 76-100. | MR

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