Abstract
Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents Hm >1/2 and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.
Original language | English |
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Pages (from-to) | 706-723 |
Number of pages | 18 |
Journal | Journal of Statistical Physics |
Volume | 152 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2013 |
Keywords
- Cluster expansion
- Fractional Brownian motion
- Long memory
- Scaling limit
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics