This book examines the long memory characteristics in the volatility of the Indian stock market, the Indian exchange rates and the Indian banking sector. This book also reviews the chain of approaches to estimate the long memory parameter. The long memory characteristics of the financial time series are widely studied and have implications for various economics and finance theories. The most important financial implication is related to the violation of the weak-form of market efficiency which encourages the traders, investors and portfolio managers to develop models for making predictions and to construct and implement speculative trading and investment strategies. In an efficient market, the price of an asset should follow a random walk process in which the price change is unaffected by ist lagged price changes and has no memory.