Rasaki, Olawale OlanrewajuAnthony, Gichuhi WaitituNafiu, Lukman Abiodun2021-05-132021-05-132021http://hdl.handle.net/20.500.12493/487This paper describes regime-switching, full range of shape changing distributions (multimodalities), and cycles traits that were characterized by time-varying series via Weibull distributional noise for time series with fluctuations and long-memory. We developed and established a Weibull Mixture Autoregressive model of k-regimes via WMAR(k; p1, p2, , pk ) with Expectation-Maximization (EM) algorithm adopted as parameter estimation technique. The ergodic process for the WMAR(k; p1, p2, , pk ) model was ascertained via the maximized derivation of the absolute value of the subtraction of its likelihood from its expected likelihood.Expectation-Maximization, k-regimes, Mixture Autoregressive model, Regime-switching, Weibull DistributionArticle