The classical Chow test for structural instability requires strictly exogenous regressors and a break-point specified in advance. In this paper, we consider two generalisations, the one-step recursive Chow test (based on the sequence of studentised recursive residuals) and its supremum counterpart, which relaxes these requirements. We use results on the strong consistency of regression estimators to show that the one-step test is appropriate for stationary, unit root or explosive processes modelled in the autoregressive distributed lags (ADL) framework. We then use the results in extreme value theory to develop a new supremum version of the test, suitable for formal testing of structural instability with an unknown break-point. The test assumes the normality of errors and is intended to be used in situations where this can be either assumed nor established empirically. Simulations show that the supremum test has desirable power properties, in particular against level shifts late in the sample and against outliers. An application to U.K. GDP data is given.
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