A NON-PARAMETRIC TEST PROCEDURE BASED ON RANGE STATISTICS TO IDENTIFY CAUSES OF NON-NORMALITY IN SPECULATIVE PRICE CHANGE DISTRIBUTIONS.

Abstract

Most models of asset pricing or market equilibrium generally require the assumption of stationary price change generation. That is, the mean and/or variance of the price change is hypothesized to be constant over time. On the other hand, the widely accepted models of speculative price change generation, such as the subordinated stochastic process models, have their basis in mixtures of random variables. These mixtures, or compositisations, define non-stationary, non-Normally distributed forms. Therefore, the models based on mixtures cannot be reconciled to requirements of stationarity. A contaminated process, such as that suggested by Mandelbroit, implies continuously changing mean and/or variance. However, an alternative concept of mixture exists, which is consistent with models requiring stationary moments. This process is referred to as slippage. Slippage defines a state where moments are constant for intervals of time, but do change value. If speculative price changes were found to be characterized by slippage, rather than by contamination, then such a finding would still be consistent with the empirical distributions of price changes. More importantly, slippage would meet the requirement of stationarity imposed on the capital market and options models. This work advanced a methodology that discriminates between contamination-based and slippage-based non-stationarity in speculative price changes. Such a technique is necessary, inasmuch as curve fitting or estimation of moments cannot so discriminate. The technique employs non-parametric range estimators. Any given form of non-Normality induces an identifiable pattern of bias upon these estimators. Once a pattern induced by a time series of price changes is identified; this pattern then infers whether contamination, or, alternatively, slippage, generated the time series. Due to the composition and technique of the procedure developed here, it is referred to as a "Range Spectrum." The results examined here find that stocks do display contamination, as hypothesized by the subordinate stochastic models. A broad based index of price change, however, displays the characteristics of slippage. This quality not only has implications for, but suggests possibilities for further research, in the areas of diversification, securities and options pricing, and market timing.