| Summary: | The classical Chow test for structural instability requires strictly exogenousregressors and a break-point specified in advance. In this paper, we consider twogeneralisations, the one-step recursive Chow test (based on the sequence of studentisedrecursive residuals) and its supremum counterpart, which relaxes these requirements. We useresults on the strong consistency of regression estimators to show that the one-step test isappropriate for stationary, unit root or explosive processes modelled in the autoregressivedistributed lags (ADL) framework. We then use the results in extreme value theory to developa new supremum version of the test, suitable for formal testing of structural instability withan unknown break-point. The test assumes the normality of errors and is intended to be usedin situations where this can be either assumed nor established empirically. Simulations showthat the supremum test has desirable power properties, in particular against level shifts latein the sample and against outliers. An application to U.K. GDP data is given.
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