Subsampling vector autoregressive tests of linear constraints

This paper studies subsampling VAR tests of linear constraints as a way of finding approximations of their finite sample distributions that are valid regardless of the stochastic nature of the data generating processes for the tests. In computing the VAR tests with subsamples (i.e., blocks of consecutive time series), both the tests of the original form and the tests with the subsample OLS coefficient estimates centered at the full-sample estimates are used. Subsampling using the latter is called centered subsampling in this paper. It is shown that the subsamplings provide asymptotic distributions that are equivalent to the asymptotic distributions of the VAR tests. In addition, the tests using critical values from the subsamplings are shown to be consistent. The subsampling methods are applied to testing for causality. To choose the block sizes for subsample causality tests, the minimum volatility method, a new simulation-based calibration rule and a bootstrap-based calibration rule are used. Simulation results in this paper indicate that the centered subsampling using the simulation-based calibration rule for the block size is quite promising. It delivers stable empirical size and reasonably high-powered causality tests. Moreover, when the causality test has a chi-square distribution in the limit, the test using critical values from the centered subsampling has better size properties than the one using chi-square critical values. The centered subsampling using the bootstrap-based calibration rule for the block size also works well, but it is slightly inferior to that using the simulation-based calibration rule.