Bayesian analysis of the model of hidden periodicities

Jiří Anděl

Kybernetika (1995)

  • Volume: 31, Issue: 1, page 1-16
  • ISSN: 0023-5954

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Anděl, Jiří. "Bayesian analysis of the model of hidden periodicities." Kybernetika 31.1 (1995): 1-16. <http://eudml.org/doc/28341>.

@article{Anděl1995,
author = {Anděl, Jiří},
journal = {Kybernetika},
keywords = {time series; model of hidden periodicities; vague prior; rectangular distribution; posterior distribution; number of periodical components},
language = {eng},
number = {1},
pages = {1-16},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bayesian analysis of the model of hidden periodicities},
url = {http://eudml.org/doc/28341},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Anděl, Jiří
TI - Bayesian analysis of the model of hidden periodicities
JO - Kybernetika
PY - 1995
PB - Institute of Information Theory and Automation AS CR
VL - 31
IS - 1
SP - 1
EP - 16
LA - eng
KW - time series; model of hidden periodicities; vague prior; rectangular distribution; posterior distribution; number of periodical components
UR - http://eudml.org/doc/28341
ER -

References

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  1. H. Z. An Z. G. Chen, E. J. Hannan, The maximum of the periodogram, J. Multivariate Anal. 13 (1983), 383-400. (1983) Zbl0517.62094MR0716931
  2. J. Anděl, Statistische Analyse von Zeitreihen, Akademie-Verlag, Berlin 1984. (1984) MR0762087
  3. E. Bølviken, New tests of significance in periodogram analysis, Scand. J. Statist. 10 (1983), 1-9. (1983) MR0711329
  4. D. R. Brillinger, Fitting cosines: some procedures and some physical examples, In: Applied Probability, Stochastic Processes and Sampling Theory (MacNeill and G. J. Umphrey, eds.), pp. 75-100, Reidel, Dordrecht 1987. (1987) 
  5. Z. G. Chen, Consistent estimates for hidden frequencies in a linear process, Adv. in Appl. Probab. 20 (1988), 295-314. (1988) Zbl0661.62094MR0938147
  6. S. T. Chiu, Detecting periodic components in a white Gaussian time series, J. Roy. Statist. Soc. Ser. B 51 (1989), 249-259. (1989) Zbl0669.62088MR1007457
  7. T. Cipra, Improvement of Fisher's test of periodicity, Apl. mat. 28 (1983), 186-193. (1983) Zbl0528.62075
  8. T. Cipra, Investigation of periodicity for dependent observations, Apl. mat. 29 (1984), 134-142. (1984) Zbl0541.62070MR0738498
  9. T. Cipra, Tests of periodicity with missing observations, Statistics 22 (1991), 233-243. (1991) Zbl0809.62079MR1097376
  10. D. Damsleth, E. Spjøtvoll, Estimation of trigonometric components in time series, J. Amer. Statist. Assoc. 77 (1982), 381-387. (1982) 
  11. F. N. David, M. G. Kendall, Tables of symmetric functions. Part I, Biometrika 36 (1949), 431-449. (1949) MR0033788
  12. M. H. DeGroot, Optimal Statistical Decisions, McGraw-Hill, New York 1970. (1970) Zbl0225.62006MR0356303
  13. R. A. Fisher, Test of significance in harmonic analysis, Proc. Roy. Soc. Ser. A 125 (1929), 54-59. (1929) 
  14. E J. Hannan, Time Series Analysis, Wiley, New York 1960. (1960) Zbl0095.13204
  15. E. J. Hannan, Testing for a jump in the spectral function, J. Roy. Statist. Soc. Ser. B 23 (1961), 394-404. (1961) Zbl0109.12801MR0137271
  16. E. J. Hannan, Non-linear time series regression, J. Appl. Probab. 8 (1971), 767-780. (1971) Zbl0227.62052MR0295498
  17. E. J. Hannan, The estimation of frequency, J. Appl. Probab. 10 (1973), 510-519. (1973) Zbl0271.62122MR0370977
  18. E. J. Hannan, M. Mackisack, A law of the iterated logarithm for an estimate of frequency, Stochastic Process. Appl. 22 (1986), 103-109. (1986) Zbl0613.60024MR0852386
  19. H. O. Hartley, Tests of significance in harmonic analysis, Biometrika 56 (1949), 194-201. (1949) Zbl0033.19104MR0034008
  20. P. L. Hsu, H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31. (1947) Zbl0030.20101MR0019852
  21. B. Kedem, Detection of periodicities by higher-order crossing, J. Time Ser. Anal. 8 (1987), 39-50. (1987) MR0868016
  22. T. Lewis, N. R. J. Fieller, A recursive algorithm for null distribution for outliers: I. Gamma samples, Technometrics 21 (1979). 371-376. (1979) MR0538441
  23. M. S. Mackisack, D. S. Poskitt, Autoregressive frequency estimation, Biometrika 76 (1989), 565-575. (1989) Zbl0674.62057MR1040649
  24. I. B. MacNeill, Tests for periodic components in multiple time series, Biometrika 61 (1974), 57-70. (1974) Zbl0275.62078MR0378317
  25. M. B. Priestley, The analysis of stationary processes with mixed spectra - I, J. Roy. Statist. Soc. Ser. B 24 (1962), 215-233. (1962) Zbl0114.08301MR0140174
  26. M. B. Priestley, Analysis of stationary processes with mixed spectra - II, J. Roy. Statist. Soc. Ser. B 24 (1962), 511-529. (1962) MR0152056
  27. B. G. Quinn, Estimating the number of terms in a sinusoidal regression, J. Time Ser. Anal. 10 (1989), 71-75. (1989) Zbl0671.62087MR1001884
  28. B. G. Quinn, J. M. Fernandes, A fast efficient technique for the estimation of frequency, Biometrika 18 (1991), 489 - 497. (1991) Zbl0737.62082MR1130917
  29. B. G. Quinn, P. J. Thomson, Estimating the frequency of a periodic function, Biometrika 18 (1991), 65-74. (1991) Zbl0717.62088MR1118231
  30. A. Schuster, On the investigation of hidden periodicities with application to the supposed 26-day period of meteorological phenomena, Terr. Magn. Atmos. Electr. 3 (1898), 13-41. 
  31. M. Shimshoni, On Fisher's test of significance in harmonic analysis, Geophys. J. R. Astronom. Soc. 23 (1971), 373-377. (1971) 
  32. A. F. Siegel, Testing for periodicity in a time series, J. Amer. Statist. Assoc. 75 (1980), 345-348. (1980) Zbl0462.62069
  33. W. F. Stout, Almost Sure Convergence, Academic Press, New York 1974. (1974) Zbl0321.60022MR0455094
  34. A. T. Walden, Asymptotic percentage points for Siegel's test statistic for compound periodicities, Biometrika 19 (1992), 438-440. (1992) 
  35. A. M. Walker, Some asymptotic results for the periodogram of a stationary time series, J. Austal. Math. Soc. 5 (1965), 107-128. (1965) Zbl0128.38701MR0177457
  36. P. Whittle, The simultaneous estimation of a time-series harmonic components and covariance structure, Trabajos Estadfst. Investigacion Oper. 3 (1952), 43-57. (1952) Zbl0049.37304MR0051487
  37. P. Whittle, The statistical analysis of a seiche record, J. of Marine Research (Sears Foundation) 13 (1954), 76-100. (1954) MR0078600
  38. G. U. Yule, On a method of investigating periodicities in disturbed series with special reference to Wolfer's sunspot numbers, Philos. Trans. Roy. Soc. London Ser. A 226 (1927), 267-298. (1927) 

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