INFERENCE IN MODELS WITH NEARLY INTEGRATED REGRESSORS

This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that c onsistently classify x as I(1) or I(0), exhibit large size distortions when regressors have local-to-unit roots, because of asymptotic depen dence on a nuisance parameter that cannot be estimated consistently. S everal alternative procedures, based on Bonferroni and Scheffe methods , are therefore proposed and investigated, For many parameter values, the power loss from using these conservative tests is small.