Rapid detection of the switching point in a financial market structure using the particle filter

We apply the particle filter for the quick and accurate estimation of a switching point in a financial market based on a recently developed theoretical model, the potentials of unbalanced complex kinetics (PUCK) model, which fulfils all empirically stylized facts such as fat-tailed distribution of price changes and the anomalous diffusion in a short-time scale. We show the efficiency of an optimized driving force in particle filtering for the estimation of the parameters of the PUCK model, using a simulation study. As an example, we apply the method to the dollar–yen exchange market before and after the biggest earthquake in Japan in March 2011. With this fast and efficient estimation method, we can clearly confirm that the statistics of the time series of exchange rate changed drastically at the time of the arrival of the quake in Tokyo area, implying that the earthquake worked as a trigger for the market's switching point.

[1]  Misako Takayasu,et al.  Predictability of currency market exchange , 2001 .

[2]  Takayuki Mizuno,et al.  Analysis of high-resolution foreign exchange data of USD-JPY for 13 years , 2003 .

[3]  Masao Nagasaki,et al.  Genomic data assimilation for estimating hybrid functional Petri net from time-course gene expression data. , 2006, Genome informatics. International Conference on Genome Informatics.

[4]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[5]  Takayuki Mizuno,et al.  Analysis of price diffusion in financial markets using PUCK model , 2007 .

[6]  T. Higuchi.  Monte carlo filter using the genetic algorithm operators , 1997 .

[7]  Afef Sellami,et al.  Comparative survey on nonlinear filtering methods: the quantization and the particle filtering approaches , 2008 .

[8]  Misako Takayasu,et al.  Random walker in temporally deforming higher-order potential forces observed in a financial crisis. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[10]  Misako Takayasu,et al.  On the nonstationarity of the exchange rate process , 2012 .

[11]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[12]  Heleno Bolfarine,et al.  Constant hazard against a change-point alternative: a bayesian approach with censored data , 1989 .

[13]  Takayuki Mizuno,et al.  Traders' strategy with price feedbacks in financial market , 2004 .

[14]  P. Cizeau,et al.  Statistical properties of the volatility of price fluctuations. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  G. Kitagawa.  Theory and Methods , 1998 .

[16]  Kazuyuki Aihara,et al.  Statistical properties of the moving average price in dollar–yen exchange rates , 2004 .

[17]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[18]  C. Gouriéroux,et al.  Non-Gaussian State-Space Modeling of Nonstationary Time Series , 2008 .

[19]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[20]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .

[21]  Misako Takayasu,et al.  The grounds for time dependent market potentials from dealers’ dynamics , 2007 .

[22]  Makoto Honda,et al.  Sequential data assimilation in geotechnical engineering and its application to seepage analysis , 2011, 14th International Conference on Information Fusion.

[23]  P. Gopikrishnan,et al.  Inverse cubic law for the distribution of stock price variations , 1998, cond-mat/9803374.

[24]  B. Mandlebrot.  The Variation of Certain Speculative Prices , 1963 .

[25]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[26]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[27]  高安 秀樹.  Practical fruits of econophysics : proceedings of the Third Nikkei Econophysics Symposium , 2006 .

[28]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[29]  Misako Takayasu,et al.  Dynamics of quote and deal prices in the foreign exchange market , 2008 .

[30]  Takayuki Mizuno,et al.  Potential force observed in market dynamics , 2006 .

[31]  H. Eugene Stanley,et al.  Inverse Cubic Law for the Probability Distribution of Stock Price Variations , 1998 .

[32]  Koichi Hamada,et al.  Statistical properties of deterministic threshold elements - the case of market price , 1992 .

[33]  G. Kitagawa.  A self-organizing state-space model , 1998 .

[34]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[35]  Fernando Estrada,et al.  Theory of financial risk , 2011 .

[36]  Misako Takayasu,et al.  Solvable stochastic dealer models for financial markets. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  MIKE WESTt,et al.  Bayesian Model Monitoring , 2010 .

[38]  Jan C. Neddermeyer.  Nonparametric particle filtering and smoothing with quasi-Monte Carlo sampling , 2011 .

[39]  Takayuki Mizuno,et al.  Theoretical analysis of potential forces in markets , 2007 .

[40]  Misako Takayasu,et al.  Characterization of foreign exchange market using the threshold-dealer-model , 2007 .

[41]  Misako Takayasu,et al.  REPLICATION OF NON-TRIVIAL DIRECTIONAL MOTION IN MULTI-SCALES OBSERVED BY THE RUNS TEST , 2012 .

[42]  Takayuki Mizuno,et al.  Theoretical Base of the PUCK-Model with Application to Foreign Exchange Markets , 2010 .

[43]  Continuum Limit and Renormalization of Market Price Dynamics Based on PUCK Model(Financial and Consumer Markets,Econophysics-Physical Approach to Social and Economic Phenomena-) , 2009 .

[44]  Tomoyuki Higuchi,et al.  Particle Filtering in Data Assimilation and Its Application to Estimation of Boundary Condition of Tsunami Simulation Model , 2009 .

[45]  Michael Isard,et al.  CONDENSATION—Conditional Density Propagation for Visual Tracking , 1998, International Journal of Computer Vision.