IDENTIFYING CAUSAL RELATIONSHIPS BETWEEN NONSTATIONARY STOCHASTIC PROCESSES: AN EXAMINATION OF ALTERNATIVE APPROACHES IN SMALL SAMPLES
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A Monte Carlo investigation is used to examine the performance of two commonly used tests for Granger causality for univariate and bivariate nonstationary ARMA (p,q) processes. Tests are applied to raw data, first differences of the raw data, and detrended versions of the series. The results indicate that for independent series the tests are robust regardless of sample size. With bivariate series and nonstationarity, the tests results are sensitive to the ARMA specification, whether the data are filtered and the type of filter used, and the sample size.