The Effect of Tick Size on Testing for Nonlinearity in Financial Markets Data

The discrete nature of financial markets time-series data may prejudice the BDS and Close Returns test for nonlinearity. Our estimation results suggest that a tick/volatility ratio threshold exists, beyond which the test results are biased. Further, tick/volatility ratios that exceed these thresholds are frequently observed in financial markets data, which suggests that the results of the BDS and CR test must be interpreted with caution.

[1]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[2]  A comprehensive examination of the compass rose pattern in futures markets , 1999 .

[3]  The Tick/Volatility Ratio as a Determinant of the Compass Rose: Empirical Evidence from Decimalisation on the NYSE , 2003 .

[4]  B. LeBaron,et al.  Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence , 1991 .

[5]  Murray Z. Frank,et al.  CHAOTIC DYNAMICS IN ECONOMIC TIME‐SERIES , 1988 .

[6]  Yue Fang.  The compass rose and random walk tests , 2002 .

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

[8]  A. Kalay,et al.  Market Making with Discrete Prices , 1998 .

[9]  Henrik Amilon.  GARCH estimation and discrete stock prices: an application to low-priced Australian stocks , 2003 .

[10]  I. Mathur,et al.  An explanation for the compass rose pattern , 2000 .

[11]  Chung-Ming Kuan,et al.  Time irreversibility and EGARCH effects in US stock index returns , 2002 .

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

[13]  Steepness and deepness in the Australian macroeconomy , 2001 .

[14]  C. Gilmore,et al.  Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory , 1996 .

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

[16]  Robust Structure Without Predictability: The "Compass Rose" Pattern of the Stock Market , 1996 .

[17]  The tick/volatility ratio as a determinant of the compass rose pattern , 2005 .

[18]  James B. Ramsey,et al.  The statistical properties of dimension calculations using small data sets , 1990 .

[19]  J. B. Ramsey,et al.  Bias and error bars in dimension calculations and their evaluation in some simple models , 1989 .

[20]  H. Saxén,et al.  Nonlinear modelling of the Finnish Banking and Finance branch index , 2004 .

[21]  Claire G. Gilmore,et al.  An examination of nonlinear dependence in exchange rates, using recent methods from chaos theory , 2001 .

[22]  Victor Chwee.  Chaos in Natural Gas Futures , 1998 .

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

[24]  Pierre L'Ecuyer,et al.  Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators , 1999, Oper. Res..

[25]  M. McKenzie,et al.  Chaotic behavior in national stock market indices: New evidence from the close returns test , 2001 .

[26]  Chaos and the compass rose , 1997 .

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

[28]  Milton S. Boyd,et al.  Testing for Chaos and Nonlinear Dynamics in Cattle Prices , 1995 .

[29]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[30]  Antonios Antoniou,et al.  Price Clustering and Discreteness: Is There Chaos Behind the Noise? , 2004, cond-mat/0407471.

[31]  Gary Gottlieb,et al.  Implications of the Discreteness of Observed Stock Prices , 1985 .