Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
979601 | Physica A: Statistical Mechanics and its Applications | 2007 | 8 Pages |
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval ΔtΔt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N . Combining these two distributions produces a non-trivial distribution of log-returns for a given time interval ΔtΔt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.