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Cumulated Sum Of Squares Statistics For Nonlinear And Nonstationary Regressions

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  • Berenguer-Rico, Vanessa
  • Nielsen, Bent

Abstract

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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  • Berenguer-Rico, Vanessa & Nielsen, Bent, 2020. "Cumulated Sum Of Squares Statistics For Nonlinear And Nonstationary Regressions," Econometric Theory, Cambridge University Press, vol. 36(1), pages 1-47, February.
    • Handle: RePEc:cup:etheor:v:36:y:2020:i:1:p:1-47_1
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    Cited by:

    1. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2024. "Out-of-sample predictability in predictive regressions with many predictor candidates," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1166-1178.
    2. James A. Duffy & Sophocles Mavroeidis & Sam Wycherley, 2022. "Cointegration with Occasionally Binding Constraints," Papers 2211.09604, arXiv.org, revised Jul 2023.
    3. Jean-Yves Pitarakis, 2020. "A Novel Approach to Predictive Accuracy Testing in Nested Environments," Papers 2008.08387, arXiv.org, revised Oct 2023.
    4. Christis Katsouris, 2022. "Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models," Papers 2202.00141, arXiv.org, revised Feb 2022.

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