Nonlinearities and Nonstationarities in Stock Returns

This article addresses the question of whether recent findings of nonlinearities in high-frequency financial time series have been contaminated by possible shifts in the distribution of the data. It applies a recursive version of the Brock–Dechert–Scheinkman statistic to daily data on two stock-market indexes between January 1980 and December 1990. It is shown that October 1987 is highly influential in the characterization of the stock-market dynamics and appears to correspond to a shift in the distribution of stock returns. Sampling experiments show that simple linear processes with shifts in variance can replicate the behavior of the tests, but autoregressive conditional heteroscedastic filters are unable to do so.

[1]  P. D. Lima,et al.  Nuisance parameter free properties of correlation integral based statistics , 1996 .

[2]  Francis X. Dieobold.  Modeling The persistence Of Conditional Variances: A Comment , 1986 .

[3]  S. Irwin,et al.  The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses , 1989, Journal of Financial and Quantitative Analysis.

[4]  Dennis W. Jansen,et al.  On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective , 1989 .

[5]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[6]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[7]  G. C. Tiao,et al.  Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance , 1994 .

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

[9]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[10]  J. Huston McCulloch,et al.  Measuring Tail Thickness to Estimate the Stable Index α: A Critique , 1997 .

[11]  S. Goldfeld,et al.  A Markov model for switching regressions , 1973 .

[12]  Evžen Kočenda,et al.  AN ALTERNATIVE TO THE BDS TEST: INTEGRATION ACROSS THE CORRELATION INTEGRAL , 2001 .

[13]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

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

[15]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[16]  F. Diebold,et al.  Modeling Volatility Dynamics , 1995 .

[17]  Jun Cai.  A Markov Model of Switching-Regime ARCH , 1994 .

[18]  Merton H. Miller.  Financial Innovations and Market Volatility , 1992 .

[19]  Jean-Guy Simonato.  Estimation of GARCH process in the presence of structural change , 1992 .

[20]  J. Huston McCulloch,et al.  13 Financial applications of stable distributions , 1996 .

[21]  S. Rachev,et al.  Modeling asset returns with alternative stable distributions , 1993 .

[22]  R. Tsay.  Outliers, Level Shifts, and Variance Changes in Time Series , 1988 .

[23]  G. Geoffrey Booth,et al.  The Stable-Law Model of Stock Returns , 1988 .

[24]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[25]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[26]  P. Phillips,et al.  Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets , 1994 .

[27]  Adrian Pagan,et al.  Testing for covariance stationarity in stock market data , 1990 .

[28]  R. Miller,et al.  On the Stable Paretian Behavior of Stock-Market Prices , 1974 .

[29]  P. D. Lima,et al.  Modeling Financial Volatility: Extreme Observations, Nonlinearities and Nonstationarities , 2000 .

[30]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .