This paper employs a combination of unit root tests and fractional integration techniques using the ARFIMA(p,d,q) model to test rational bubbles, which implies herd behavior, in Bombay Stock Exchange (BSE). The results in the paper strongly support the evidence of herd behavior in the daily, weekly, and monthly price aggregates. Moreover, the paper also investigates the degree of conditional volatility persistence using FIGARCH(p,d,q) specification to show that the persistence of shocks to stock price and dividend yield volatilities is short-termed.