Fréchet Random Noise for k-Regime-Switching Mixture Autoregressive Model
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
American Journal of Mathematics and Statistics
Abstract
This paper describes Fréchet distribution as a random noise for capturing multimodalities, regime-switching and
change-points attributed to uniformly time-varying series via causality of fluctuations, extreme values and heavy-tailed time
series. Fréchet Mixture Autoregressive (FMAR) model of k-regime-switching, denoted by FMAR(k; p1, p2 ,, pk ) was
developed and Expectation-Maximization (EM) algorithm was used as a method of parameter estimation for the embedded
coefficients of AR of k-mixing weights and lag pk. The limiting distribution of the FMAR(k; p1, p2 ,, pk ) model via
Gnedenko-Fisher Tippet limiting property was derived to asymptotically approach an exponential function.
Description
Keywords
Fréchet distribution, Expectation-Maximization, Gnedenko-Fisher Tippet, k-regime-switching, Mixture Autoregressive, Multimodalities