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Spectral analysis of climatological time series: On the performance of periodogram, non-integer and maximum entropy methods

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Summary

Three independent techniques used in spectral analysis of time series, the conventional periodogram, the maximum entropy spectral analysis and the non-integer method, are applied to a drought index time series and the results are compared. The results reveal that in general the three approaches give similar estimates, especially in the high frequency domain.

The main drawback of the periodogram method is its poor frequency resolution, especially in case of short records. Consequently, while the position of the sinewave frequencies computed by the periodogram seems accurate, the peaks are broad mainly because of the limited length of the data sample. The maximum entropy spectral analysis on the other hand, gives better frequency resolution than either the periodogram or the non-integer method. This method is, however, sensitive to the number of terms of the filter and this has a great influence on the quality of the spectrum.

The non-integer spectra are comparable to higher order maximum entropy spectra. However, because the lowest frequency at which the non-integer spectra can be estimated is the inverse of the length of record, their spectra (for short records) may not be as reliable as those resolved by the maximum entropy spectral analysis in the low frequency domain.

Overall, it is suggested that the maximum entropy spectral analysis is preferable to either the periodogram or the noninteger method when one deals with short climatological time series. A good practice will be to compare the results of the maximum entropy with those of the non-integer method in order to strengthen inferences about the nature of periodicity in the analysed climatological time series.

Zusammenfassung

Drei unabhängige Techniken werden in Spektralanalysen von Zeitreihen verwendet: Die konventionelle Periodogramm-Methode, die Maximalentropie-Spektralanalyse und die Non-Integer-Methode werden auf Zeitserien des Trockenheits-Index angewandt und die Resultate verglichen. Diese Resultate zeigen, daß die drei Verfahren grundsätzlich zu vergleichbaren Ergebnissen führen, v.a. im Hochfrequenz-Bereich.

Der wesentliche Nachteil der Periodogramm-Methode ist ihre Frequenzungenauigkeit, besonders im Fall kurzer Aufzeichnungszeiträume. Daraus folgt, daß die im Periodogramm ausgewiesenen Positionen der Sinuskurven-Frequenzen genau zu stimmen scheinen, die Spitzen aber ungenau bleiben, v. a. auf Grund begrenzter Datenerhebungen.

Die Maximalentropie-Spektralanalyse wiederum weist höhere Frequenzgenauigkeit als die beiden anderen Methoden auf, reagiert jedoch äußerst sensibel auf die Anzahl der Filterterme wodurch die Qualität der Spektren stark beeinflußt wird.

Die Non-Integer-Spektren sind den Maximalentropie-Spektren höherer Ordnung vergleichbar. Da jedoch die niedrigste Frequenz, die auf den Non-Integer-Spektren gemessen werden kann, reziprok zur Aufzeichnungsdauer ist, sind diese Spektren (bei kurzer Aufzeichnungsdauer) im Niederfrequenzbereich nicht so zuverlässig wie jene der Maximalentropie-Spektralanalysen.

Daraus ergibt sich, daß bei Vorliegen kurzer klimatologischer Zeitserien der Maximalentropie-Spektralanalyse der Vorzug vor den beiden anderen Methoden zu geben ist. Ein Vergleich der Ergebnisse der Maximalentropie mit jenen der Non-Integer-Methode scheint empfehlenswert, da dies verstärkt Rückschlüsse auf die Art der Periodiziät in den untersuchten klimatologischen Zeitreihen erlaubt.

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  1. Department of Geography, Ahmadu Bello University, Zaria, Nigeria

    E. O. Oladipo

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Oladipo, E.O. Spectral analysis of climatological time series: On the performance of periodogram, non-integer and maximum entropy methods. Theor Appl Climatol 39, 40–53 (1988). https://doi.org/10.1007/BF00867656

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