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Spectral analysis of Markov switching GARCH models with statistical inference

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  • Maddalena Cavicchioli

Abstract

We derive matrix expressions in closed form for the autocovariance function and the spectral density of Markov switching GARCH models and their powers. For this, we apply the Riesz–Fischer theorem which defines the spectral representation as the Fourier transform of the autocovariance function. Under suitable assumptions, we prove that the sample estimator of the spectral density is consistent and asymptotically normally distributed. Further statistical implications in terms of order identification and parameter estimation are discussed. A simulation study confirms the validity of the asymptotic properties. These methods are also well suited for financial market applications, and in particular for the analysis of time series in the frequency domain, as shown in some proposed real‐world examples.

Suggested Citation

  • Maddalena Cavicchioli, 2023. "Spectral analysis of Markov switching GARCH models with statistical inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 102-119, March.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:1:p:102-119
    DOI: 10.1111/sjos.12571
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