The Behavior of Stock-Price Relatives—A Markovian Analysis

This paper presents a method of Markovian analysis of changes in the natural logarithms of stock prices over time. It examines 200 stocks from the New York Stock Exchange for the period December 23, 1963, to November 29, 1968, and defines a set of three states (up, down, small change) for the process in terms of the mean absolute deviation of changes in the natural logarithms of prices. This definition of the set of states allows both the magnitude and the direction of change to be incorporated in the analysis. Standard statistical tests for stationarity and dependence in vector and individual-process Markov-chain models are employed for both fixed- and variable-time data (the latter refers to highs for a day or week interval). In addition, a method for testing the homogeneity of the vector Markov chain is given. Empirical results for the vector-process model suggest that price movements appear to be described by a first- or higher-order nonstationary Markov chain. Tests also indicate that the vector-process Markov chain is heterogeneous. Empirical results for the individual-process Markov-chain model suggest that an individual stock has a short-term memory with respect to daily price relatives, i.e., the process is first-or higher-order. However, the corresponding process lacks stationarity. No dependency appears to exist for a weekly time lag.