Some theoretical properties of share price time series

In this article, the author develops a simple stock-market model of a stochastic type and derives a few of its statistical properties. Particular attention has been given to those properties relevant to the random walk hypothesis of share prices. The basic premise of this article is that the quantity demanded and the quantity supplied of a share are both a function of price and another variable representing the effect of information. In the first section of the article, the author describes the model. Diverse types of information can affect the market price of a share, ranging from the obvious specific news content of a change in the directors' board of a firm to more global events. It would be impossible to list explicitly all the variables which may affect the quantity demanded or supplied at a given price, so one may conveniently represent these effects by random variables. The derivations are heavily dependent on properties of random variables, and that these properties hold quite independently of the economic interpretation of the model. It is well known, and is intuitively obvious, that the first difference of a random series is negatively autocorrelated