This paper, authored by Peter King Clark, explores the characteristics of speculative prices, particularly focusing on the leptokurtic nature of price changes and the violation of the Central Limit Theorem. The author argues that price changes in speculative markets, such as futures in commodities or corporation shares, are not normally distributed due to their leptokurtic distribution, which has too many small and large observations. Clark introduces the concept of subordinated stochastic processes, where the distribution of price changes is subordinate to a normal distribution. This means that the number of individual effects contributing to price changes varies, leading to a non-constant number of terms in the sum of price changes. The paper develops a generalized Central Limit Theorem for processes with random numbers of terms and shows that the distribution of these processes still converges to a normal distribution under certain conditions. The paper also discusses the distribution of lognormal-normal increments, which is found to fit the observed distribution of cotton price changes better than the normal distribution. The author tests the hypothesis that trading volume measures the speed of evolution of the price process and finds a curvilinear relationship between trading volume and price change variance. This suggests that the "imperfect clock" hypothesis, where trading volume is used as an instrument for the true operational time, is a good approximation. Finally, the paper presents a Bayesian test and a Kolmogorov-Smirnov test to compare the lognormal-normal distribution with stable distributions. The results strongly support the finite-variance subordination model, indicating that the observed leptokurticity in price change distributions is due to the data being recorded in "clock" time rather than operational time.This paper, authored by Peter King Clark, explores the characteristics of speculative prices, particularly focusing on the leptokurtic nature of price changes and the violation of the Central Limit Theorem. The author argues that price changes in speculative markets, such as futures in commodities or corporation shares, are not normally distributed due to their leptokurtic distribution, which has too many small and large observations. Clark introduces the concept of subordinated stochastic processes, where the distribution of price changes is subordinate to a normal distribution. This means that the number of individual effects contributing to price changes varies, leading to a non-constant number of terms in the sum of price changes. The paper develops a generalized Central Limit Theorem for processes with random numbers of terms and shows that the distribution of these processes still converges to a normal distribution under certain conditions. The paper also discusses the distribution of lognormal-normal increments, which is found to fit the observed distribution of cotton price changes better than the normal distribution. The author tests the hypothesis that trading volume measures the speed of evolution of the price process and finds a curvilinear relationship between trading volume and price change variance. This suggests that the "imperfect clock" hypothesis, where trading volume is used as an instrument for the true operational time, is a good approximation. Finally, the paper presents a Bayesian test and a Kolmogorov-Smirnov test to compare the lognormal-normal distribution with stable distributions. The results strongly support the finite-variance subordination model, indicating that the observed leptokurticity in price change distributions is due to the data being recorded in "clock" time rather than operational time.