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 |
|---|---|
| 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 |
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Keywords
- Cluster expansion
- Fractional Brownian motion
- Long memory
- Scaling limit
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market. / Kuroda, Koji; Maskawa, Jun ichi; Murai, Joshin.
In: Journal of Statistical Physics, Vol. 152, No. 4, 08.2013, p. 706-723.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market
AU - Kuroda, Koji
AU - Maskawa, Jun ichi
AU - Murai, Joshin
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
KW - Cluster expansion
KW - Fractional Brownian motion
KW - Long memory
KW - Scaling limit
UR - http://www.scopus.com/inward/record.url?scp=84881030834&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84881030834&partnerID=8YFLogxK
U2 - 10.1007/s10955-013-0783-z
DO - 10.1007/s10955-013-0783-z
M3 - Article
AN - SCOPUS:84881030834
VL - 152
SP - 706
EP - 723
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 4
ER -