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Jointly testing linearity and nonstationarity within threshold autoregressions

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  • Pitarakis, Jean-Yves

Abstract

We develop a test of the joint null hypothesis of linearity and nonstationarity within a threshold autoregressive process of order one with deterministic components. We derive the limiting distribution of a Wald type test statistic and subsequently investigate its local power and nite sample properties. We view our test as a useful diagnostic tool since a non rejection of our null hypothesis would remove the need to explore nonlinearities any further and support a linear autoregression with a unit root.

Suggested Citation

  • Pitarakis, Jean-Yves, 2012. "Jointly testing linearity and nonstationarity within threshold autoregressions," MPRA Paper 38845, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38845
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    References listed on IDEAS

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    1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    2. Jean-Yves Pitarakis, 2008. "Comment on: Threshold Autoregressions With a Unit Root," Econometrica, Econometric Society, vol. 76(5), pages 1207-1217, September.
    3. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    4. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    5. Pitarakis, Jean-Yves, 2011. "Joint Detection of Structural Change and Nonstationarity in Autoregressions," MPRA Paper 29189, University Library of Munich, Germany.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Cited by:

    1. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    2. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.

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    More about this item

    Keywords

    Threshold Autoregressive Models; Unit Roots; Near Unit Roots; Brownian Bridge; Augmented Dickey Fuller Test;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • 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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