Sample size, lag order and critical values of seasonal unit root tests

A response surface analysis for the distributions of popular tests for seasonal unit roots in quarterly observed time series variables is presented. Five test statistics are considered, along with the most commonly used specifications of the deterministic component in the test regression; allowance is also made for the lag order in the test regression to be determined endogenously, using commonly applied selection methods. Response surface coefficients are reported, permitting simple computation of accurate critical values for 1%-, 5%- and 10%-level tests and probability values for any sample size and lag order. Accurate approximations of the asymptotic distributions are obtained in the process of constructing the response surfaces. Dependence of the critical values and the probability density functions on the sample size and lag order is investigated.