Author(s): Olanrewaju O Rasaki, Oseni Ezekiel, Adekola Lanrewaju Olumide and Oyinloye Adedeji Adigun

Abstract: This study describes the approach for modeling extreme and lengthy time-varying series of an Autoregressive Moving Average of order (p, q) via a Skew Generalized Extreme Value distribution as the white noise. This approach establishes the procedure for parameters’ estimation and their standard errors for the SGEV-ARMA (p, q) model via the iterative Fisher information scores derived from the Maximum Likelihood Estimation for a chosen optimal degree of flexibility (bandwidth) "S" . The study was applied to a lengthy series of average monthly temperature (report in ^oC) of Lagos, Nigeria from January 1901 to December 2016 with 1381 data points. It was noted that SGEV-ARMA (3,3) recorded a subjacent model performance error via the evaluated indexes of AIC, BIC and HQIC (103.02, 141.35 & 124.50) respectively compare to an intensive error performance in the white noise Gaussian-ARMA (3, 3) with (108, 144.4 & 129.26) respectively. In addition, the forecast error indexes with the SGEV subjected white noise were miniaturized compared to the Gaussian white noise.

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