Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2003
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| _version_ | 1866912655081472000 |
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| author | Ivanova, K. Ausloos, M. Takayasu, H. |
| author_facet | Ivanova, K. Ausloos, M. Takayasu, H. |
| contents | The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and $JPY/DEM$ and $DEM/USD$ currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these financial time series we perform a statistical analysis of their increments $Δx(Δ(t))$ distribution functions for different time lags $Δ(t)$. From the probability distribution functions at various $Δ(t)$, the Fokker-Planck equation for $p(Δx(t), Δ(t))$ is explicitly derived. It is written in terms of a drift and a diffusion coefficient. The Kramers-Moyal coefficients, are estimated and found to have a simple analytical form, thus leading to a simple physical interpretation for both drift $D^{(1)}$ and diffusion $D^{(2)}$ coefficients. The Markov nature of the indices and exchange rates is shown and an apparent difference in the NASDAQ $D^{(2)}$ is pointed out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cond_mat_0301268 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach Ivanova, K. Ausloos, M. Takayasu, H. Statistical Mechanics Numerical Analysis Chaotic Dynamics Computational Physics Statistical Finance The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and $JPY/DEM$ and $DEM/USD$ currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these financial time series we perform a statistical analysis of their increments $Δx(Δ(t))$ distribution functions for different time lags $Δ(t)$. From the probability distribution functions at various $Δ(t)$, the Fokker-Planck equation for $p(Δx(t), Δ(t))$ is explicitly derived. It is written in terms of a drift and a diffusion coefficient. The Kramers-Moyal coefficients, are estimated and found to have a simple analytical form, thus leading to a simple physical interpretation for both drift $D^{(1)}$ and diffusion $D^{(2)}$ coefficients. The Markov nature of the indices and exchange rates is shown and an apparent difference in the NASDAQ $D^{(2)}$ is pointed out. |
| title | Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach |
| topic | Statistical Mechanics Numerical Analysis Chaotic Dynamics Computational Physics Statistical Finance |
| url | https://arxiv.org/abs/cond-mat/0301268 |