Summary
Forty-two monthly rainfall time series from Spain have been analyzed for the presence of cycles and regional patterns. The study was carried out by means of periodicity tests devised by Whittle, Hannan, Bartlett, Siegel, and Priestley. These tests contribute to a mixed spectrum analysis leading to the evaluation of signals versus the background of ‘coloured’ noise (autocorrelation). Also, a direct maximum entropy method (MEM) for estimating spectra was applied to the series, in particular an autoregressive (AR) power spectral density (psd) estimation, and an autoregressive moving average (ARMA) psd estimation, with parameters obtained by exact maximum likelihood estimator (MLE).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike, H., 1971: Information theory and an extension of the maximum likelihood principle.Research Memorandum No. 46, Institute of Statistical Mathematics, Tokyo. Published in 2nd Int. Symp. on Inf. Theory (Eds. B. N. Petrov and F. Csaki), 267–281. Akademiai Kiade, Budapest (1973).
Akaike, H., 1974: A new look at the statistical model identification.IEEE Trans. Automatic Control AC-19, 716–722.
Bartlett, M. S., 1955:An Introduction to Stochastic Processes with Special Reference to Methods and Applications. London: Cambridge University Press.
Bhansali, R. J., 1977: An application of Priestley'sP(γ) test to the southern tide heights data. In: Barra, J. R. et al. (ed.)Recent Developments in Statistics. Amsterdam: North-Holland, 351–356.
Bhansali, R. J., 1979: A mixed spectrum analysis of the linx data.J. Roy. Statist. Soc. Ser. A 142, (2), 199–209.
Blackman, R. B., Tukey, J. W., 1959:The Measurement of Power Spectra From the Point of View of Communications Engineering. New York: Dover.
Bloomfield, P., 1976:Fourier Analysis of Time Series: An Introduction. New York: John Wiley & Sons, 258 pp.
Burg, J. P., 1967: Maximum entropy spectral analysis.Proc. 37th Meeting Society of Exploration Geophysicists, Oklahoma City, OK.
Burg, J. P., 1975:Maximum Entropy Spectral Analysis. Ph.D. dissertation, Dep. Geophysics, Stanford Univ., Stanford, CA.
Cooley, J. W., Tukey, J. W., 1965: An algorithm for machine calculation of complex Fourier series.Math. Comput. 19, 297–301.
Currie, R. G., 1989: Comments on ‘Power spectra and coherence of drought in the interior plains by E. O. Oladipo’.J. Climatol. 9, 91–100.
Currie, R. G., O'Brien, D. P., 1988: Periodic 18.6 year and cyclic 10 to 11 year signals in Northeastern United States Precipitation Data.J. Climatol. 8, 255–281.
Currie, R. G., O'Brien, D. P., 1990: Deterministic signals in precipitation records from the American corn belt.J. Climatol. 10, 179–189.
Fisher, R. A., 1929: Tests of significance in harmonic analysis.Proc. R. Soc., Ser. A 125, 54–59.
Hannan, E. J., 1961: Testing for a jump in the spectral function.J. Roy. Statist. Soc. B 23, 394–404.
Hannan, E. J., 1970:Multiple Time Series. New York: John Wiley and Sons, 536 pp.
Jaynes, E. T., 1982: On the rationale of maximum entropy methods.Proc. IEEE 70, 939–952.
Jaynes, E. T., 1983: In: Rosenkrantz, R. D. (ed.)Papers on Probability, Statistic, and Statistical Physics. Hingham: D. Riedel.
Jenkins, G. M., Priestley, M. B., 1957: The spectral analysis of time-series.J. Roy. Statist. Soc. B 19, 1–12.
Jenkins, G. M., Watts, D. G., 1968:Spectral Analysis and its applications. San Francisco: Holden Day, 525 pp.
Kay, S. M., Marple, S. L., Jr, 1981: Spectrum analysis — a modern perspective.Proc. IEEE 69, 1380–1419.
Parzen, E., 1968: Statistical spectral analysis (single channel case).Dep. Statistics, Standford, CA. Tech. Rep. 11.
Press, H., Houlboult, J. C., 1955: Some applications of generalised harmonic analysis to gust loads on airplanes.J. Aerosol. Sci. 22, 17–26.
Press, H., Tukey, J. W., 1956: Power spectral methods of analysis and their application to problems in airplane dynamics.Bell Systems Monograph No. 2606.
Priestley, M. B., 1962a: The analysis of stationary processes with mixed spectra-I.J. Roy. Statist. Soc. B 24, 215–233.
Priestley, M. B., 1962b: The analysis of stationary processes with mixed spectra-II.J. Roy. Statist. Soc. B 24, 511–529.
Priestley, M. B., 1964: Estimation of the spectral density function in the presence of the harmonic components.J. Roy. Statist. Soc. B 26, 123–132.
Priestley, M. B., 1981:Spectral Analysis and Time Series. London: Academic Press, 890 pp.
Shuster, A., 1898: On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena.Terr. Magn. 3, 13–41.
Siegel, A. F., 1980: Testing for periodicity in a time series.J. Amer. Statist. Assoc. 75, 345–348.
Whittle, P., 1952: The simultaneous estimation of a timeseries harmonic components and covariance structure.Trab. Estad. 3, 43–57.
Whittle, P., 1954: The statistical analysis of a seiche record.J. Marine Research (Sears Foundation) 13, 76–100.
Wold, H. O. A., 1954:A Study in the Analysis of Stationary Time Series, 2nd ed. Stockholm: Almqvist and Wiksell.
Author information
Authors and Affiliations
Additional information
With 4 Figures
Rights and permissions
About this article
Cite this article
Garrido, J., García, J.A. Periodic signals in Spanish monthly precipitation data. Theor Appl Climatol 45, 97–106 (1992). https://doi.org/10.1007/BF00866398
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00866398