Browsing by Author "Anthony, Gichuhi Waititu"

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    Fréchet Random Noise for k-Regime-Switching Mixture Autoregressive Model
    (American Journal of Mathematics and Statistics, 2021) Rasaki, Olawale Olanrewaju; Anthony, Gichuhi Waititu; Nafiu, Lukman Abiodun
    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.
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    On the Estimation of k-Regimes Switching of Mixture Autoregressive Model via Weibull Distributional Random Noise
    (International Journal of Probability and Statistics, 2021) Rasaki, Olawale Olanrewaju; Anthony, Gichuhi Waititu; Nafiu, Lukman Abiodun
    This 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.