The presence of long range persistence and its impact on policy decisions are examined in the Indian Forex market during the period between 2000 and 2015. Hurst-Mandelbrot's Classical R/S Statistic, Lo Statistic, Robinson's Estimate have been computed. Long memory in volatility and absolute return series of each currency pair were evidenced but the logarithmic return series of all these currency pairs indicate proclivity towards the “random walk” hypothesis. Therefore, currencies are not systematically over- or under-valued, which provides justification for passive index investment in these currencies. However, possibilities of speculation/hedging activities could not be ruled out which may call Reserve Bank’s intervention and interest smoothing behavior with potentials for impaired price discovery.