Long Memory in Rupee-Dollar Exchange Rate Returns: A Robust Analysis

Financial time series like exchange rates are highly persistent. An unexpected shock to the underlying variable has long lasting effects. The persistence in the volatility of the time series is usually exemplified by a highly persistent fitted GARCH model. Traditional stationary ARMA processes often cannot capture the high degree of persistence in financial time series. In the last few years, more applications have evolved using long memory processes, which lie halfway between traditional stationary I (0) processes and the non-stationary I (1) processes. There is substantial evidence that long memory processes can provide a good description of many highly persistent financial time series. This study examines last 37 years of continuous log returns of INR-USD exchange rates for long memory effect. R/S test statists confirms the presence of long memory effect, parameters are estimated using Whittle's method. Further analysis shows that only long memory component with fractionally integrated FARIMA is not stable and short memory component are required to make makes model stable. Tests prove that FARIMA (2, 0.004, 0) explains the variations best in case of Rupee-Dollar exchange rate returns.