For regression models alternative asymptotically equivalent misspecification tests may lead to conflicting inference in small samples. Effective misspecification tests should have correct significance levels irrespective of the true parameters and any redundant regressors in the model, and reasonable power against a wide class of alternative specifications. A simulation study of various tests for serial correlation and predictive failure in models with lagged dependent variables finds many tests defective in small samples. Only particular degrees of freedom adjustments to the test statistics yield improved small sample behaviour.

The authors consider the relative bias of the OLS-based estimate s(squared) of the disturbance variance in the linear regression model when disturbances are stationary AR(1). They improve upon previous bounds for the bias and show that E(s[squared]/[sigma squared]) tends to zero as autocorrelation increases whenever there is an intercept in the regression.

Methods are proposed to build exact tests and confidence sets in the linear first-order autoregressive distributed lag model with i.i.d. disturbances. For general linear hypotheses on the regression coefficients, inference procedures are obtained which have known level. The tests proposed are either similar (i.e., they have constant rejection probability for all data generating processes consistent with the null hypothesis) or use bounds which are free of nuisance parameters. Correspondingly the confidence sets are either similar with known size (i.e., they have constant coverage probability) or conservative. We also develop exact tests and confidence sets for various nonlinear transformations of model parameters, such as long-run multipliers and mean lags. The practical usefulness of these exact methods, which are also asymptotically valid under weak regularity conditions, is illustrated by some power comparisons and with applications to a dynamic trend model of money velocity and a model of money demand.