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Tests for Harmonic Components in the Spectra of Categorical Time Series

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  • Monnie McGee
  • Katherine Ensor

Abstract

A test for categorical time series is developed which is based on Fisher’s test for continuous‐parameter time series. Instead of using a test based on the Fourier periodog ram for spectral analysis, we utilize the Walsh–Fourier periodogram for testing purposes. We briefly explain the theory behind Walsh–Fourier analysis and some of its recent applications. Asymptotic results for the distribution of the new test statistic for Walsh–Fourier spectra are presented and compared with a simulated distribution. We also perform power studies in order to assess the detection capability of the test. In the presence of multiple peaks in the spectrum, this test tends to lose power. Therefore, we also explore several alternatives to the test for Walsh–Fourier spectra and apply all of the alternative methods to a realization of geomagnetic reversals

Suggested Citation

  • Monnie McGee & Katherine Ensor, 1998. "Tests for Harmonic Components in the Spectra of Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 309-323, May.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:3:p:309-323
    DOI: 10.1111/1467-9892.00094
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    Cited by:

    1. Kim C. Raath & Katherine B. Ensor, 2023. "Wavelet-L2E Stochastic Volatility Models: an Application to the Water-Energy Nexus," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 150-176, May.

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