A bootstrap test for causality with endogenous lag length choice: theory and application in finance

Granger causality tests have become among the most popular empirical applications with time series data. Several new tests have been developed in the literature that can deal with different data generating processes. In all existing theoretical papers it is assumed that the lag length is known a priori. However, in applied research the lag length has to be selected before testing for causality. This paper suggests that in investigating the effectiveness of various Granger causality testing methodologies, including those using bootstrapping, the lag length choice should be endogenized, by which we mean the data-driven preselection of lag length should be taken into account. We provide and accordingly evaluate a Granger-causality bootstrap test which may be used with data that may or may not be integrated, and compare the performance of this test to that for the analogous asymptotic test. The suggested bootstrap test performs well and appears to be also robust to ARCH effects that usually characterize the financial data. This test is applied to testing the causal impact of the US financial market on the market of the United Arab Emirates.