Rasaki, Olawale OlanrewajuAnthony, Gichuhi WaitituNafiu, Lukman Abiodun2021-05-132021-05-132021http://hdl.handle.net/20.500.12493/488This 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.Fréchet distribution, Expectation-Maximization, Gnedenko-Fisher Tippet, k-regime-switching, Mixture Autoregressive, MultimodalitiesArticle