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  • Vanessa Berenguer-Rico (a1) and Bent Nielsen (a1)


We show that the cumulated sum of squares statistic has a standard Brownian bridge–type asymptotic distribution in nonlinear regression models with (possibly) nonstationary regressors. This contrasts with cumulated sum statistics which have been previously studied and whose asymptotic distribution has been shown to depend on the functional form and the stochastic properties, such as persistence and stationarity, of the regressors. A recursive version of the test is also considered. A local power analysis is provided, and through simulations, we show that the test has good size and power properties across a variety of situations.


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*Address correspondence to Bent Nielsen, Nuffield College, Oxford, OX1 1NF, UK; e-mail:


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Comments from Giuseppe Cavaliere and the referees are gratefully acknowledged.



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