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.

An extensive study has been carried out on the returns of time series data using Autoregressive Integrated Moving Average (ARIMA), Generalized Autoregressive Conditional Heteroscedastic (GARCH) models during the last two decades. Earlier studies are mainly based on analysis using historical data and graphs (Diebold and Nerlove, 1989; and Harvey, 1990), and some are analysis using fundamental macroeconomic relations. This technical analysis uses only historical time series data like ex post exchange rates to determine the trend and to model volatility.

This approach goes against the efficient market hypothesis due to 'Random Walks' (Nelson and Plosser, 1982) present in Time Series. The efficient market hypothesis states that the time series variables reflect all the available information that can be obtained through various sources which are already reflected in prices and no one can predict the future movements. On the other hand, the Random Walk theory also suggests that past information cannot be used as a guideline to predict the future movements of the time series variables (Darrat, 1990). Despite these assertions, many multinational companies, foreign exchange dealers, exporters, importers and speculators continue to make hedging decisions based on the patterns existing in the ex post data with the expectation that these provide an indication of future movement of exchange rates at least in the short run. If such patterns exist, then it is possible to apply modern econometric tools such as ARIMA and GARCH to forecast ex anti exchange rates (Hamilton, 1994).

ARIMA was introduced by Box and Jenkins during the 1960s for forecasting a variable. ARIMA method is an extrapolation method for forecasting, and like any such method, it requires only the historical time series data on the variable under forecasting. This is one of the sophisticated extrapolation methods, since it incorporates the features of all other methods. However, it does not require the investigator to choose the initial values of any variable and values of various parameters a priori. Further, it is robust to handle any data pattern. As one would expect, this is quite a difficult model to develop and apply, as it involves transformation of the variable, identification of the model, estimation through non-linear method, verification of the model and derivation of forecasts. This paper attempts to estimate an ARIMA model based on Autoregressive Conditional Heteroscedasticity (ARCH), GARCH for exchange rate in the economy of India and after that a comparison between RBI forecast error and the GARCH-based ARIMA forecast.

Bank Management Journal, RBI Forecast, Indian Rupee, Globalization, US Dollar Exchange Rate, Foreign Exchange Risk Management, Autoregressive Conditional Heteroscedasticity Model, Regression Models, Atheoretic Models, Economic Variables, Partial Autocorrelation Functions.