A new statistic and practical guidelines for nonparametric Granger causality testing

Upon illustrating how smoothing may cause over-rejection in nonparametric tests for Granger non-causality, we propose a new test statistic for which problems of this type can be avoided. We develop asymptotic theory for the new test statistic, and perform a simulation study to investigate the properties of the new test in comparison with its natural counterpart, the Hiemstra-Jones test. Our simulation results indicate that, if the bandwidth tends to zero at the appropriate rate as the sample size increases, the size of the new test remains close to nominal, while the power remains large. Transforming the time series to uniform marginals improves the behavior of both tests. In applications to Standard and Poor's index volumes and returns, the Hiemstra-Jones test suggests that volume Granger-causes returns. However, the evidence for this gets weaker if we carefully apply the recommendations suggested by our simulation study.

[1]  D. Tjøstheim,et al.  Nonparametric tests of serial independence , 1993 .

[2]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

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

[4]  Relationships between Australian real estate and stock market prices—a case of market inefficiency , 2002 .

[5]  Thomas M. Stoker,et al.  Optimal bandwidth choice for density-weighted averages , 1996 .

[6]  Cointegration and Detectable Linear and Nonlinear Causality: Analysis Using the London Metal Exchange Lead Contract , 2004 .

[7]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[8]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[9]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[10]  Craig Hiemstra,et al.  Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation , 1994 .

[11]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[12]  Yue Ma,et al.  Testing for a nonlinear relationship among fundamentals and exchange rates in the ERM , 2000 .

[13]  Cees Diks,et al.  A Note on the Hiemstra-Jones Test for Granger Non-causality , 2005 .

[14]  B. Pompe.  Measuring statistical dependences in a time series , 1993 .

[15]  Joel L. Horowitz,et al.  An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative , 2001 .

[16]  M. Denker,et al.  On U-statistics and v. mise’ statistics for weakly dependent processes , 1983 .

[17]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[18]  H. White,et al.  A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE , 2008, Econometric Theory.

[19]  Jim Malley,et al.  A non-parametric approach to non-linear causality testing , 1996 .

[20]  Imad A. Moosa,et al.  The relationship between spot and futures prices: Evidence from the crude oil market , 1999 .

[21]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[22]  Chris Brooks.  Predicting stock index volatility: can market volume help? , 1998 .

[23]  Abhay Abhyankar.  Linear and nonlinear Granger causality: Evidence from the U.K. stock index futures market , 1998 .

[24]  P. Wilson,et al.  The Causal Relationship Between Real Estate and Stock Markets , 2000 .

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

[26]  Cetin Ciner,et al.  Energy Shocks and Financial Markets: Nonlinear Linkages , 2001 .