RBI Forecast Vs. GARCH-Based ARIMA Forecast for Indian Rupee-US Dollar Exchange Rate: A Comparison

Foreign exchange risk management is a new challenging area. After globalization, the perfection in exchange rate forecasting is very essential for hedging decisions. In this paper, an attempt has been made to estimate the parameters of Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and apply them to simulate and predict the rupee/US dollar exchange rates. The emphasis of these methods is not on constructing single equation or simultaneous-equation models but on analyzing the probabilistic or stochastic properties of economic time series on their own under the philosophy of letting the data speak for themselves. As a matter of fact, many econometric time series exhibit periods of unusually large volatility, followed by periods of relative tranquility. In such circumstances, the assumption of homoscedasticity is inappropriate. It is a particular kind of the Heteroscedasticity in which the variance of the regression error depends on the volatility of the errors in the recent past. Engle suggested the use of Autoregressive Conditional Heteroscedasticity (ARCH) model to take care of such Heteroscedasticity in order to raise the efficiency of forecasts. Many of the lagged values of unconditional error variance can be replaced with one or two lagged values of conditional error variance. This leads to the GARCH model. The main objective of this paper is to study the GARCH-based minimum mean squared error ARIMA forecast for rupee/dollar exchange rate and draw a comparison between ARIMA, GARCH-based ARIMA and RBI forecasting.