Exact tests for structural change in first-order dynamic models

Several finite-sample tests of parameter constancy against the presence of structural change are proposed for a linear regression model with one lagged dependent variable and independent normal disturbances. The procedures derived include analysis-of-covariance, CUSUM, CUSUM-of-squares, and predictive tests. The approach used to obtain the tests involves the application of three techniques: derivation of an exact confidence set for the autoregressive parameter (based on using an appropriately extended regression), a union-intersection technique, and (when required) randomization. The tests proposed are illustrated with some artificial data and applied to a dynamic trend model of gross private domestic investment in the U.S.