Generalized cross-spectral test for nonlinear Granger causality with applications to money-output and price-volume relations

- This paper first proposes a new spectral analytical instrument-the generalized cross spectral distribution function.
- We develop a new test for linear and nonlinear Granger causality, which has no problem of “curse of dimensionality”.
- Monte Carlo simulation shows that our proposed test has better size and power performance than Hong's (2001) test.
- The empirical studies show that, the proposed test statistic succeeds in capturing the nonlinear Granger causality.

In this study, we propose a test statistic based on a generalized cross-spectral distribution function to test for linear and nonlinear Granger causality. The test statistic considers all time series lags and, at the same time, avoids the “curse of dimensionality” problem. Moreover, it avoids having to choose a kernel function and bandwidth parameter. Since the generalized cross-spectral distribution test statistic asymptotically converges to a nonstandard distribution, we propose a wild bootstrap approach to approximate its critical values. A Monte Carlo simulation shows that the generalized cross-spectral distribution test statistic has better finite sample performance than Hong's (2001) test. In the empirical analysis, we perform empirical tests for Granger causality between U.S. money and output and between the return and volume of the CSI 300 Index and show that the proposed test statistic succeeds in capturing nonlinear Granger causality.