Modeling exchange rate volatility using EM algorithm with hybrid GARCH models

Ali Salman  Habeeb

doi:https://doi.org/10.59139/stattrans-2026-031

Modeling exchange rate volatility using EM algorithm with hybrid GARCH models

Ali Salman Habeeb 1Department of Statistics, University of Sumer, Dhi Qar Governorate, Al-Rifai, Iraq ORCID:https://orcid.org/0000-0003-0037-8292 Statistics in Transition new series, vol. 27, 2026, 3, pages: 135-155 Published online: 9 September 2026 https://doi.org/10.59139/stattrans-2026-031 Citation: Habeeb A. S., 2026. Modeling exchange rate volatility using EM algorithm with hybrid GARCH models. Statistics in Transition new series, 27(3), pp. 135-155. https://doi.org/10.59139/stattrans-2026-031

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ABSTRACT

The most important basic tools for modeling and analyzing econometric models are linear and nonlinear time series analyses, with the aim of formulating an accurate probabilistic model that expresses the behavior of the phenomenon over a specific time period. In this study, we construct a three-step hybrid probability model that includes model identification, model estimation, and diagnosis checking using the Box-Jenkins approach. We explored the performance of two important tools for estimating unknown parameters of the proposed model. The first is Maximum Likelihood (ML), which has a wide reputation in the statistical literature, and is provided in Eviews10 software. Furthermore, we compared it with the second proposed numerical method, namely Expectation-Maximization (EM algorithm), which requires creating a special MATLAB code to implement its performance. Moreover, we compared two methods using information criteria (AIC, BIC, HQ). In order to show the effectiveness of the hybrid ARCH-GARCH models, we used them to measure the volatility of the weekly exchange rate of the Central Bank of Iraq’s sales of the US dollar against the Iraqi dinar from the first week of 2021 to the last week of 2023. We concluded that the appropriate model is the hybrid MA(1)-GARCH(1,1) model, which is represented by the Moving Average MA(1) of the average equation and the GARCH(1,1) model of the conditional variance equation.

KEYWORDS

time series analysis, exchange rate volatility, maximum likelihood, expectationmaximization( EM algorithm), generalized autoregressive conditional heteroscedasticity

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