This is one of the most methods which can be used for testing the evidence of the weak form of efficiency. If the returns of the stock price are serially correlated then the investor can predict the future stock price path with the help of the past information and this can be a violation to the weak form of efficient market hypothesis. The stock price returns can exhibit either positive serial correlation or can exhibit negative serial correlation. Using serial correlation to trade can be a form of technical analysis which the investor uses to predict the stock price movement.
Different researchers have done their research on this and come out with different conclusions. A study done by Kendall in the year 1953 and also by Roberts in the year 1959 suggested that they did not find any serial correlation which existed in the stocks. They covered a wide range of stock markets.
However, in another study done by researcher Lo with another researcher Mackinlay, they found that there exists positive serial correlation in the prices of the stocks listed on the New York Exchange. They found this positive serial correlation in the weekly returns for the stock prices. However the amount of serial correlation calculated by them did not offer much chance of the trading opportunities.