Numerous empirical studies have appeared in recent years concerning the behavior of stock market prices. Cootner's book [2] presents an excellent summary of pre-1964 efforts, while Fama's paper [5] discusses some of the more recent work. While a few writers believe that certain price trends and patterns exist which enable the investor to make better predictions of the expected value of future stock price changes, the majority of these studies conclude that past price data alone cannot form the basis for the prediction of the expected value of price movements in the stock market.

This paper has discussed the importance of stationary data in statistical applications and has at the same time suggested one method for testing for stationarity. An application of the testing procedure is made to common stock prices. The results indicate that these data could be nonstationary in the usual sense of stability of the mean and mean-square values despite efforts to transform the data into a stationary form using first differences.

The efficient market, martingale model of security price movements requires that the arrival of new information be promptly arbitraged away. A necessary and sufficient condition for the existence of an arbitraged price is that statistical dependence among prices must decrease very rapidly. If persistent statistical dependence is present, the arbitraged price changes do not follow a martingale and should have an infinite variance. Using a technique for detecting long-term dependence, called R/S analysis, 200 daily stock return series are studied; many series are characterized by long-term dependence. Thus, in the presence of long-term dependence, the martingale model does not hold. Also, the distribution of security returns is non-normal stable Paretian as opposed to Gaussian.