Modelling and Forecasting the Volatility of Daily Exchange Rate Using GARCH Model

Abstract

The volatility of daily exchange rate is a significant economic indicator for open economic countries like Sri Lanka, when considering the international level trade. Therefore, it is very important to be aware of the behavior of future fluctuations of the exchange rate volatility, even though accurate volatility forecasting is challenging. The purpose of this study is to model and forecast the volatility of the US Dollar against the Sri Lankan Rupee (USD/LKR) daily exchange rate. The daily USD/LKR exchange rate data from 1st January 2015 to 30th April 2021 were used in this study and it was found that the exchange rate was continuously increasing throughout the period and stationarity of the daily exchange rate return series was confirmed by the Augmented Dickey-Fuller (ADF) test. Volatility of the daily exchange rate returns were modeled using Generalized Auto-Regressive Conditional Heteroscedastic (GARCH) models. ARMA(2,1) was found to be the most preferable model for the mean equation, and GARCH(1,1) was identified to be best to capture the conditional volatility of the residuals of the ARMA(2,1) model. In addition, Lagrange Multiplier (LM) test clearly showed that ARCH effect no longer exists in the residuals of ARMA(2,1) - GARCH(1,1) model and the Sign Bias test indicated that there was no asymmetry effect in residuals. Therefore ARMA(2,1) - GARCH(1,1) was identified as the best model to forecast the USD/LKR daily exchange rate with Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) equal to 0.047695, 0.218391, and 0.047695 respectively. The findings of this study can be used in decision and policy making stages to minimize the risk associated with exchange rate volatility.