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

Abduljabbar Ali Mudhir

doi:10.24996/ijs.2021.62.7.19

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.

Highlights

As a general description of this research, we will show how to mix the equation model of ARMA model with the variance equation of the conditional variance model and compose a mixed model that controls the linear and nonlinear behaviors of the series that contains volatility in its data
There are a lot of efforts in modeling this behavior, most of which being successful, but the autoregressive conditional heteroscedasticity (ARCH) model was the most favorable due the simplicity of its formulas and interpretation of the analysis of time series that has fluctuations in its data
Table-4 presents results of the numerical test and Ljung-Box test for squared standard residuals series with h=0, which implies unaccepting the rejection of the null hypothesis ( ), i.e. accepting it. This refers to the removal of the heteroscedasticity effect, where the p-value is higher than. These results show that the residuals series of EGARCH(3,3) model is uncorrelated and homoscedastic

Summary

Introduction

As a general description of this research, we will show how to mix the equation model of ARMA model with the variance equation of the conditional variance model and compose a mixed model that controls the linear and nonlinear behaviors of the series that contains volatility in its data. A. Iraqi Journal of Science, 2021, Vol 62, No 7, pp: 2307-2326 new hypothesis, called the heteroscedasticity hypothesis, was created and many mathematical models were suggested for linear and nonlinear time series, such as ARCH models and its generalized (GARCH) models for Engle 1982[1] and Bollerslev 1986[2], respectively, TAR models for Tong. The autoregressive conditional heteroscedasticity (ARCH) model has a great importance globally because it has been used in modeling and analyzing the behavior of big changes in modern phenomena, such as the accompanying risks of returns for the financial time series, as in those of gold and oil prices, volume trading, and inflation. There are a lot of efforts in modeling this behavior, most of which being successful, but the ARCH model was the most favorable due the simplicity of its formulas and interpretation of the analysis of time series that has fluctuations in its data

Objectives

Discussion

Conclusion