The performance of MRS-GARCH models : a ML and Bayesian MCMC-based estimations

Abstract

This study compared the in-sample and out-of-sample forecasting accuracy of nonlinear MRS-GARCH forecasting model using two estimation methods namely: The Maximum Likelihood and the Bayesian Markov Chain Monte Carlo. In addition, the study fitted an appropriate model that best describes the volatility of the exchange rates of BRICS countries. Data used was obtained from the Quantec Data Company. It covered the period from 1997 to 2017 with a total of 241 observations. Various tests of nonlinearity and nonlinear unit root were used to assess the validity of the assumptions of the study. Specifically, the study used a battery of linearity tests including Regression Specification Error Test (RESET), ARCH test, the McLeod and Li, Keenan's, Tsay, Brock- Dechert-Scheinkman (BDS), and CUSUM tests to determine whether or not exchange rates exhibit asymmetric behaviour. The Bierens Nonlinear Augmented Dickey-Fuller (B-NADF) and Kapetanois-Schmidt-Shin Nonlinear Augmented Dickey-Fuller (KSS-NADF) were applied to determine whether the time series properties of exchange rates of BRICS countries were nonlinear and have nonlinear unit root in nature. To choose the best fitted model, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Log-likelihood (LOGL) and Deviance information criterion (DIC) were employed under different conditional distributions for innovation. Furthermore, the Mean Square Error (MSE), Mean absolute Error (MAE) and Root Mean Square Error (RMSE) served as the error measures in evaluating the forecasting ability of the models. The MRS-GARCH models proved to perform well with lower error measures when the Bayesian framework is used with student-t distribution for in-sample and for out-of-sample generalized error distribution. The decision by error measures were supported by Diebold and Mariano test of predictive accuracy. The results showed that the Bayesian method produces accurate and reliable forecasts. In this study, the Bayesian method is preferred over Maximum Likelihood estimation method. The findings of the study proved both the Maximum Likelihood Estimation, and the Bayesian Markov Chain Monte Carlo estimation methods are good estimators, even though further improvement is evident. In the case of Maximum Likelihood Estimation method, where Expected Maximization (EM) algorithm was used, the study recommended that the Monte Carlo Maximum Likelihood estimator and/or Monte Carlo Expected Maximization estimator

can be used to improve Maximum Likelihood estimation method. The results from these two methods may be compared with those of the previous studies.