Tuesday, June 3, 2014

Cootner, The Random Character of Stock Market Prices, III

Herewith some excerpts from Paul Cootner’s introduction to Part II, “Refinement and Empirical Testing.”

* * *

“Despite Bachelier’s very early interest in stochastic analysis of speculative prices and Working’s renewed interest in the 1920’s, stock market research from this point on was very slow to develop. While professional practitioners displayed a strong and continuing interest in the stock market, it enjoyed relatively little academic attention until after the debacle of 1929. While such lack of attention was not absolute, it stands out very sharply in comparison with the extensive research on commodity prices and on prices of those financial instruments which came under the rubric of 'money.' This disinterest was compounded of many parts: the smaller role played by organized equity markets in industrial finance, a conviction that stock markets were the product of mass (irrational) psychology akin to gambling, and a shortage, among economists, of the mathematical and statistical skills necessary for effective research in this field.

“These last two reasons bulk particularly large. When research into stock prices did attract renewed attention in the 1930’s, most of it focused among the same American economists who were important in the embryo school of economists interested in the use of mathematics and statistics. Aside from Working, the major name in this period is that of Alfred Cowles. The Cowles Commission (now Foundation) organized the first major collection of statistical data on the U.S. stock market resulting in the publication of Common Stock Indexes published in 1938. Even before that publication, however, Cowles has begun to analyze stock prices from the unique point of view that motivates this collection.

“What research into stock prices had come before was largely devoted to attempts to predict such prices based on 'outside' data, whether earnings, industrial production, or sunspots. While Cowles was interested in somewhat related phenomena, such as the predictive ability of stock brokers’ market letters, a major part of his research focused on the question of forecasting stock market prices from the past history of prices themselves. It may be worthwhile to dwell on this distinction since it is sometimes a source of confusion among nonexperts. When statisticians hypothesize that the course of stock prices describes a random walk or Brownian motion, they do not imply that a skilled student of the subject cannot forecast price changes. They merely imply that one cannot forecast the future based on past history alone.” (pp. 79-80)

“Because of [the upward long-term trend of the market], any large sample of price changes contains more positive changes than negative. As a result, in any study of runs, there is a greater tendency for positive changes to be followed by positive changes (long up-runs) and a smaller tendency for negative changes to be followed by negative changes (shorter down-runs) than would be found in a series with zero mean. The significant differences found by Cowles are indicative of this general uptrend rather than a serial dependence among price changes after correction for such trend.” (p. 81)

“The publication in 1959 of both the Roberts and Osborne papers marked the beginning of the sharp recent increase in interest in this subject, by bringing it to the attention of the American academic audience for the first time since Cowles’ articles in the thirties. Although attention was an important factor in stimulating interest, the soil had been fertilized in an important way by the widening introduction of electronic computing machinery.” (p. 82)

“… Moore’s work strongly supports the results found previously by Kendall and Osborne. Autocorrelation coefficients are uniformly small and usually quite insignificant; runs tests support the independence hypothesis, and the distribution of price changes seemed at least approximately log-normal. The careful testing did, however, yield some mildly disturbing evidence which was to become more important in the research and theories of future students. For one thing, the distributions of price changes, while ‘close’ to normal, showed a consistent tendency for more large price changes than expected. For another, autocorrelations of successive one-week changes, while individually statistically insignificant, are predominantly negative to a degree which is statistically significant. Actually, Kendall’s empirical results with price indexes had foreshadowed this, although in the case of indexes, the overwhelming number of autocorrelations at one-week intervals were positive, becoming predominantly negative at longer intervals.

“C. W. J. Granger and O. Morgenstern’s paper on spectral analysis brings into play modern techniques of time series analysis which had previously been confined to data in the physical sciences. The spectrum of a time series is a representation (through Fourier transforms) of the autocorrelation function of that series. In that respect it is a close, if more sophisticated relative of the correlelogram. Within the limitations of available data, the spectrum gives a complete picture of autocorrelation in any stationary stochastic process with finite variance. It also determines the best linear predictor for such a time series. If, however, the series is not stationary, or if its variance does not exist (Mandelbrot, 1963), the results may be ambiguous or incorrect. Also the failure to find any linear predictive relation does not rule out the possibility (Alexander, 1961) that a nonlinear relation exists. With these provisos in mind, however, the Granger-Morgenstern research lends strong support to the random walk thesis.” (p. 83)

No comments:

Post a Comment