Recurrence quantification analysis and state space divergence reconstruction for financial time series analysis

The application of recurrence quantification analysis (RQA) and state space divergence reconstruction for the analysis of financial time series in terms of cross-correlation and forecasting is illustrated using high-frequency time series and random heavy-tailed data sets. The results indicate that these techniques, able to deal with non-stationarity in the time series, may contribute to the understanding of the complex dynamics hidden in financial markets. The results demonstrate that financial time series are highly correlated. Finally, an on-line trading strategy is illustrated and the results shown using high-frequency foreign exchange time series.

[1]  Strozzi Fernanda,et al.  Non-linear Trading Strategy for Financial Time Series , 2006 .

[2]  Joseph P. Zbilut,et al.  On-line runaway detection in isoperibolic batch and semibatch reactors using the divergence criterion , 2004, Comput. Chem. Eng..

[3]  Francesco Lisi,et al.  Is a random walk the best exchange rate predictor , 1997 .

[4]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[5]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[6]  Fernanda Strozzi,et al.  Non-linear forecasting in high-frequency financial time series , 2005 .

[7]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[8]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[9]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[10]  Joseph P. Zbilut,et al.  Early warning detection of runaway initiation using non-linear approaches , 2005 .

[11]  Abdol S. Soofi,et al.  Nonlinear deterministic forecasting of daily dollar exchange rates , 1999 .

[12]  J. L. Nolan,et al.  Numerical calculation of stable densities and distribution functions: Heavy tails and highly volatil , 1997 .

[13]  Joseph P. Zbilut,et al.  Application of Nonlinear Time Series Analysis Techniques to High-Frequency Currency Exchange Data. , 2002 .

[14]  A. Giuliani,et al.  Recurrence quantification analysis of the logistic equation with transients , 1996 .

[15]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[16]  Fernanda Strozzi,et al.  Towards a non-linear trading strategy for financial time series , 2006 .

[17]  A. N. Sharkovskiĭ.  Dynamic systems and turbulence , 1989 .

[18]  R Hegger,et al.  Denoising human speech signals using chaoslike features. , 2000, Physical review letters.

[19]  N. Johnson,et al.  Financial market complexity , 2003 .

[20]  V. Arnold,et al.  Ordinary Differential Equations , 1973 .

[21]  Gao,et al.  Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Fernanda Strozzi,et al.  On-Line Runaway Detection in Batch Reactors Using Chaos Theory Techniques. , 1999 .

[23]  John Okunev,et al.  Do Momentum-Based Strategies Still Work in Foreign Currency Markets? , 2003, Journal of Financial and Quantitative Analysis.

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

[25]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[26]  C. Diks.  Nonlinear time series analysis , 1999 .

[27]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[28]  F. Strozzi,et al.  Recurrence quantification based Liapunov exponents for monitoring divergence in experimental data , 2002 .

[29]  Rosario N. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[30]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[31]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[32]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .