Regime switching of mixture autoregressive process for discretized time events

Abstract

This paper establishes the need for Poisson random noise for mixture autoregressive process for strictly discretized time events (count series), and as well possessed traits of regime switching, and multimodalities that are usually caused by jumps, fluctuations, and outliers. Consequently, a Poisson mixture autoregressive (PMAR) model with k-regimes, denoted by PMAR(k : p1, p2, . . . , pk) was established and developed, such that, the embedded associated k-regime autoregressive and Poisson coefficients were estimated via Expectation-Maximization (EM) algorithm. The limiting distribution (asymptotic property) of the PMAR(k : p1, p2, . . . , pk) process was ascertained via the Central Limit Theorem (CLT) as well as the lower bound variance estimator of the PMAR process. The model was applied to the significant wave height of the Belmullet Inner (Berth B) and Belmullet Outer (Berth A) of the Atlantic Ocean. The discretized time events of the berths gave a realization of two regimes switching for Berth A and B respectively. The second regime produced a minimum Mean Square Error (MSE) of 12.02 compared to 12.32 produced by first regime.