Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models

Abstract

This paper aims to make a comparison between range-based and return-based volatility models. For this purpose, we compare the Conditional Autoregressive Range (CARR) type and Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models with different innovation distributions and the Exponential Weighted Moving Average (EWMA) model with fixed and estimated lambda parameters. The out-of-sample forecasts obtained from the volatility processes are compared according to the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Heteroskedastic Root Mean Square Error (HRMSE), and Heteroskedastic Mean Absolute Error (HMAE) statistics. We use the USD-TRY exchange rate data for real-life applications since estimating the volatility of forex helps to determine prices for goods and services to avoid the uncertainty created by exchange rate shocks in developing countries such as Turkiye. Although MAE and RMSE show Gumbel CARR and Weibull CARR have the minimum error statistics, respectively, the HMAE and HRMSE statistics indicate that among the range-based models, the EWMA model, in which the lambda parameter is estimated, performs better. Furthermore, we find that Exponential CARR according to RMSE and MAE statistics, and Weibull CARR according to HMAE and HRMSE statistics appear as the return-based volatility models with minimum error.