Fréchet Random Noise for k-Regime-Switching Mixture Autoregressive Model

摘要

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 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 p _(k ). The limiting distribution of the model via Gnedenko-Fisher Tippet limiting property was derived to asymptotically approach an exponential function.