Exact tests in single equation autoregressive distributed lag models

For hypotheses on the coefficient values of the lagged-dependent variables in the ARX class of dynamic regression models, test procedures are developed which yield exact inference for given (up to an unknown scale factor) distribution of the innovation errors. They include exact tests on the maximum lag length, for structural change and on the presence of (seasonal or multiple) unit roots, i.e. they cover situations where usually asymptotic and non-exact t, F, AOC, ADF or HEGY tests are employed. The various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed.