Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory

Interest in the relevance of nonlinear dynamics to fields such as finance and economics has spurred the development of new methods of analysis for time series data. Early tests for chaos led to problems when applied to financial and economic data. This motivated development of the BDS family of statistics to test for nonlinearity generally. More recently, another method of analysis has been introduced into the scientific literature. It uses a test for chaos which is relatively simple and appropriate for financial data. A quantitative version of this test is developed here and is used to analyze stock return data.

[1]  Robert Savit,et al.  When random is not random: An introduction to chaos in market prices , 1988 .

[2]  L. Summers.  Does the Stock Market Rationally Reflect Fundamental Values , 1986 .

[3]  Claire G. Gilmore,et al.  A new test for chaos , 1993 .

[4]  Gautam Kaul,et al.  Mean Reversion in Short-Horizon Expected Returns , 1989 .

[5]  R. Gilmore,et al.  Topological analysis and synthesis of chaotic time series , 1992 .

[6]  W. Brock,et al.  Is the business cycle characterized by deterministic chaos , 1988 .

[7]  Murray Z. Frank,et al.  Measuring the Strangeness of Gold and Silver Rates of Return , 1989 .

[8]  J. Poterba,et al.  Mean Reversion in Stock Prices: Evidence and Implications , 1987 .

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

[10]  K. French.  Stock returns and the weekend effect , 1980 .

[11]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[12]  Josef Lakonishok,et al.  Are Seasonal Anomalies Real? A Ninety-Year Perspective , 1988 .

[13]  A. Lo,et al.  Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test , 1987 .

[14]  E. Fama,et al.  Permanent and Temporary Components of Stock Prices , 1988, Journal of Political Economy.

[15]  E. Fama,et al.  Efficient Capital Markets : II , 2007 .

[16]  G. Mindlin,et al.  Classification of strange attractors by integers. , 1990, Physical review letters.

[17]  Gabriel B. Mindlin,et al.  Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction , 1991 .

[18]  David Hsieh.  Chaos and Nonlinear Dynamics: Application to Financial Markets , 1991 .

[19]  David Ruelle,et al.  Deterministic chaos: the science and the fiction , 1995 .

[20]  R. Shiller.  Stock Prices and Social Dynamics , 1984 .

[21]  James B. Ramsey,et al.  Economic and financial data as nonlinear processes , 1988 .

[22]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[23]  R. Roll.  Vas Ist Das? , 1983 .

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

[25]  David Hsieh.  Testing for Nonlinear Dependence in Daily Foreign Exchange Rates , 1989 .

[26]  W. Brock.  Distinguishing random and deterministic systems: Abridged version , 1986 .

[27]  G. Schwert.  Why Does Stock Market Volatility Change Over Time? , 1988 .

[28]  N. Tufillaro,et al.  Relative rotation rates: Fingerprints for strange attractors. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[29]  V. Akgiray.  Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts , 1989 .

[30]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[31]  Hidekatsu Tokumaru,et al.  Autocorrelations of a certain chaos , 1980 .

[32]  B. LeBaron,et al.  Nonlinear Dynamics and Stock Returns , 2021, Cycles and Chaos in Economic Equilibrium.

[33]  Donald B. Keim.  SIZE-RELATED ANOMALIES AND STOCK RETURN SEASONALITY Further Empirical Evidence , 1983 .

[34]  Claire G. Gilmore,et al.  A NEW APPROACH TO TESTING FOR CHAOS, WITH APPLICATIONS IN FINANCE AND ECONOMICS , 1993 .

[35]  Philip Rothman,et al.  The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications , 1990 .

[36]  Narasimhan Jegadeesh,et al.  Seasonality in Stock Price Mean Reversion: Evidence from the U.S. and the U.K. , 1991 .

[37]  R. Ariel,et al.  High Stock Returns before Holidays: Existence and Evidence on Possible Causes , 1990 .

[38]  Sherrill Shaffer,et al.  Structural shifts and the volatility of chaotic markets , 1991 .

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

[40]  K. French,et al.  Expected stock returns and volatility , 1987 .

[41]  Bruce Mizrach,et al.  On Determining the Dimension of Real-Time Stock-Price Data , 1992 .

[42]  M. Hénon,et al.  A two-dimensional mapping with a strange attractor , 1976 .

[43]  Jess Benhabib,et al.  Chaos: Significance, Mechanism, and Economic Applications , 1989 .

[44]  R. Thaler,et al.  Does the Stock Market Overreact , 1985 .

[45]  J. Poterba,et al.  Mean Reversion in Stock Prices: Evidence and Implications , 1987 .

[46]  Douglas M. Patterson,et al.  Evidence of Nonlinearity in Daily Stock Returns , 1985 .

[47]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[48]  Ted Jaditz,et al.  IS CHAOS GENERIC IN ECONOMIC DATA , 1993 .