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Keywords:

  • stock price;
  • long-range dependence;
  • self-similarity;
  • Hurst parameter

The influence of the behavior and strategies of traders on stock price formation has attracted much interest. It is assumed that there is a positive correlation between the total net demand and the price change. A buy order is expected to increase the price, whereas a sell order is assumed to decrease it. We perform data analysis based on a recently proposed stochastic model for stock prices. The model involves long-range dependence, self-similarity, and no arbitrage principle, as observed in real data. The arrival times of orders, their quantity, and their duration are created by a Poisson random measure. The aggregation of the effect of all orders based on these parameters yields the log-price process. By scaling the parameters, a fractional Brownian motion or a stable Levy process can be obtained in the limit. In this paper, our aim is twofold; first, to devise statistical methodology to estimate the model parameters with an application on high-frequency price data, and second, to validate the model by simulations with the estimated parameters. We find that the statistical properties of agent level behavior are reflected on the stock price, and can affect the entire process. Moreover, the price model is suitable for prediction through simulations when the parameters are estimated from real data. The methods developed in the present paper can be applied to frequently traded stocks in general. Copyright © 2013 John Wiley & Sons, Ltd.