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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. Jean-Yves Pitarakis, 2017. "A Simple Approach for Diagnosing Instabilities in Predictive Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 851-874, October.
    2. Pitarakis, Jean-Yves & Gonzalo, Jesús, 2020. "Out of sample predictability in predictive regressions with many predictor candidates," UC3M Working papers. Economics 31554, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Jean-Yves Pitarakis, 2020. "A Novel Approach to Predictive Accuracy Testing in Nested Environments," Papers 2008.08387, arXiv.org.

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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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