Using the high-frequency data of Bitcoin, this paper investigates the long memory characteristics of the unconditional and conditional volatilities of Bitcoin at different time scales using the local Whittle (LW) estimator, the exact local Whittle (ELW) estimator and the ARMA–FIAPARCHmodel. The results show that the long memory parameter is significant and quite stable for both unconditional and conditional volatility measures across different time scales. This paper also examines the long memory characteristics of the unconditional and conditional “realized” volatilities of Bitcoin at different time scales using the local Whittle (LW) estimator, exact local Whittle (ELW) estimator and the ARFIMA model. Long memory is found to be significant and stable also in case of unconditional and conditional “realized” volatilities. The study also undertakes quarterly non-overlapping rolling window analysis to develop deeper insights into the evolution of long memory parameter, d, over the period. The results indicate high persistence in the Bitcoin market. This study has useful implications for different investors and market participants having varying exposures in the Bitcoin market depending on their trading horizons. The findings can help them in forecasting the expected volatility in the Bitcoin market and thereby in developing and implementing trading strategies.