Autoregressive Integrated Moving Average (ARIMA) processes of various orders are presented to identify an optimal model from a class of models. Parameters of the models are estimated using an Ordinary Least Square (OLS) approach. ARIMA (p, d, q) is formulated for maximum daily temperature data in Ondo and Zaira from January 1995 to November 2005. The choice of ARIMA models of orders p and q is intended to retain persistence in a natural process. To determine the performance of models, Normalized Bayesian Information Criterion is adopted. The ARIMA (1, 1, 1) is adequate for modeling maximum daily temperature in Ondo and Zaira; model parameters are estimated and redundant variables are removed. Causality and the invertibility behavior of some optimal models are also presented.