The GARCH-X(1,1) Model with Exponentially Transformed Exogenous Variables

Abstract

This study applies the exponential transformation to the exogenous variables in the GARCH-X(1,1) model. The model assumes that the returns error is Normally and Student-t distributed. The data type used as an exogenous variable in the GARCH-X(1,1) model is Realized Volatility 10 minutes. Empirical analysis was carried out based on stock price index data FTSE100 and SP500 daily period from January 2000 to December 2021. Metropolis Adaptive Random Walk method was implemented in the Markov Chain Monte Carlo algorithm to estimate the model parameters. The High Posterior Density interval at the 95% level indicates the significance of the exponential transformation for the exogenous variable in both cases assuming a distribution for the returns error. Moreover, the Akaike Information Criterion (AIC) value indicates that the proposed model outperforms the basic GARCH-X(1,1) model, where the best fit model is given by the Student-t distributed model.