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

Purpose: In all existing theoretical papers on causality 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. The purpose of this paper is to suggest 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. Design/methodology/approach: The size and power of a bootstrap test with endogenized lag-length choice are investigated by simulation methods. A statistical software component is produced to implement the test, which is available online. Findings: The simulation results show that this test performs well. An application of the test provides empirical support for the hypothesis that the UAE financial market is integrated with the US market. Social implications: The empirical results based on this test are expected to be more precise. Originality/value: This paper considers a bootstrap test for causality with endogenous lag order. This test has superior properties compared to existing causality tests in terms of size, with similar if not better power and it is robust to ARCH effects that usually characterize financial data. Practitioners interested in causal inference based on time series data might find the test valuable.