This paper develops a robust causality test for time series with infinite variance innovation processes. First, we introduce a measure of dependence for vector nonparametric linear processes, and derive the asymptotic distribution of the test statistic by Taniguchi et al. (1996) in the infinite variance case. Second, we construct a weighted version of the generalized empirical likelihood (GEL) test statistic, called the self-weighted GEL statistic in the time domain. The limiting distribution of the self-weighted GEL test statistic is shown to be the usual chi-squared one regardless of whether the model has finite variance or not. Some simulation experiments illustrate satisfactory finite sample performances of the proposed test.
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