Asymptotic Tests for Univariate Random Walk Coefficients in Models with Stationary Regressors
Martin Moryson · Contributions to statistics · 1998
The tests proposed so far are all exact tests in the sense that their null distribution can be assessed exactly. This is an obvious advantage as one does not have to appeal to asymptotic arguments to justify these tests. On the other hand, these exact tests have severe drawbacks: they are difficult to compute and they rest on rather strict assumptions. The null distributions of the LBI and the POI test depend on the data, i.e. one cannot tabulate critical values, they have to be computed for each testing problem anew, as outlined in section 3.6. Especially, if T becomes large this can be very time consuming and numerically difficult. In the case of the LaMotte & McWhorter (1978) F -test the difficulty lies not in determining the exact critical values but rather in the calculation of the test statistic itself. One has to determine the ( T × (T—k)) matrix P whose columns form an orthogonal basis for the vector subspace orthogonal to X . This matrix is rather difficult to compute. Even though many computer programs offer build in routines it remains a time and work space consuming task and is potentially unstable if T becomes large. Even though this matrix is not necessary for the calculation of the POI and LBI test statistics it is necessary for the computation of the critical values of these. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.