An extensive empirical study has been conducted on Indian stock markets data towards model based investigations on characterization of time series in this work. The financial time series dataused in this research study were from the two leading Indian stock exchanges of India namely National Stock Exchange of India limited (NSE) and Bombay Stock Exchange limited (BSE). Totally 230 time series data were studied and analyzed for modeling and forecasting. These 230 time series comprised of 32 index price series listed in NSE, 16 index price series from BSE and 50 price series of companies listed in NSE. Frequency wise the data included 98 daily price series and 66 price series of monthly and weekly each. The data were obtained up to the period of December 2012 from the respective available starting date.