Mixing ARMA Models with EGARCH Models and Using it in Modeling and Analyzing the Time Series of Temperature

Abstract

In this article our goal is mixing ARMA models with EGARCH models and composing a mixed model ARMA(R,M)-EGARCH(Q,P) with two steps, the first step includes modeling the data series by using EGARCH model alone interspersed with steps of detecting the heteroscedasticity effect and estimating  the model's parameters and check the adequacy of the model. Also we are predicting the conditional variance and verifying it's convergence to the unconditional variance value. The second step includes mixing ARMA with EGARCH and using the mixed (composite) model in modeling time series data and predict future values then asses the prediction ability of the proposed model by using prediction error criterions.