Long range dependence in the high frequency USD/INR exchange rate

Using high frequency data, this paper examines the long memory property in the unconditional and conditional volatility of the USD/INR exchange rate at different time scales using the Local Whittle (LW), the Exact Local Whittle (ELW) and the FIAPARCH models. Results indicate that the long memory property remains quite stable across different time scales for both unconditional and conditional volatility measures. Results from the non-overlapping moving window approach indicate that the extreme events (such as the subprime crisis and the European debt crisis) resulted in highly persistent behavior of the USD/INR exchange rate and thus lead to market inefficiency. This paper also examines the long memory property in the realized volatility based on different time scale data. Results indicate that the realized volatility measures based on different scales of the high frequency data exhibit a consistent and stable long memory property. However, the realized volatility measures based on daily data exhibit lower degree of long-range dependence. This study has implications for traders and investors (with different trading horizons) and can be helpful in predicting expected future volatility and in designing and implementing trading strategies at different time scales.