This study investigates the stock price behavior of Indian stock markets using BSE Sensex as well as 30 individual underlying shares included in the Sensex. Variance Ratio test for the market index suggests dependency of the aggregate market series, which violates the assumption of Random Walk Hypothesis (RWH). However, the test results manifest mixed behavior of return generating process for individual companies. Sixteen companies have been found to show dependence while the remaining 14 companies could be described by the RWH. The study has also developed one forecasting model for the market index using the ARIMA process. The AR(9) model has been found to be an appropriate model for forecasting future returns to the Sensex, the validity of which is of course, subject to real-world experiments.

For many years, financial economists have been interested in developing and testing models of stock price behavior. One important model that has evolved from this research is the theory of Random Walk. To test Random Walk Hypothesis (RWH), one can examine the patterns of short-term movements in return series and attempt to identify the process underlying those returns. Acceptance of this hypothesis implies that stock prices are independent and one is unable to identify a pattern. On the other hand, rejection of the hypothesis has serious implications for investors, as it is possible to establish a pattern where past data can be used to predict future market movements, and thereby, one can earn profits from forecasting future prices.

A considerable body of finance literature has tested the efficient markets model by examining individual autocorrelations and applying runs test in security returns. The early tests surveyed by Fama (1970), found little evidence of patterns in security returns and is frequently adduced in support of the efficient markets hypothesis. Recent work by Shiller and Perron (1985) and Summers (1986) has shown that such tests have relatively little power against interesting alternative hypothesis of market efficiency, which led to the evolution of a new generation of tests.

Several recent studies using new tests for serial dependence have rejected the random walk model in the US market. Lo and MacKinlay (1988) found that stock returns do not follow random walks for the US markets using a variance ratio test. Poterba and Summers (1988) suggest that the values of variance ratios give evidence of negative autocorrelations (mean reversion) at long investment horizons and positive autocorrelations at short horizons.