This study analyses the long memory properties of daily returns on S&P CNX Nifty and its volatility. Absolute returns and squared returns are used as the proxies of the volatility. The fractional integration parameters are estimated using the GPH and the local-Whittle estimators. The index returns do not show the long memory properties. On the other hand, the variables representing volatility show highly significant fractional integration. However, the estimated values of fractional integration parameters do not show stability across the sub-sample periods. Unstable distribution of fractional integration parameter suggests that the observed long memory in volatility is possibly caused by structural breaks rather than the true fractional integration.