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Dickey–Fuller Type of Tests against Nonlinear Dynamic Models

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  • Changli He
  • Rickard Sandberg

Abstract

In this paper, we introduce several test statistics testing the null hypothesis of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure and the trend. We derive analytical limiting distributions for all the tests. The power performance of the tests is compared with that of the unit‐root tests by Phillips and Perron [Biometrika (1988), Vol. 75, pp. 335–346], and Leybourne, Newbold and Vougas [Journal of Time Series Analysis (1998), Vol. 19, pp. 83–97]. In the presence of a gradual change in the deterministics and in the dynamics, our tests are superior in terms of power.

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  • Changli He & Rickard Sandberg, 2006. "Dickey–Fuller Type of Tests against Nonlinear Dynamic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 835-861, December.
    • Handle: RePEc:bla:obuest:v:68:y:2006:i:s1:p:835-861
    DOI: 10.1111/j.1468-0084.2006.00459.x
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    References listed on IDEAS

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    1. Markku Lanne & Helmut Lütkepohl & Pentti Saikkonen, 2003. "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(1), pages 91-115, February.
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    8. He, Changli & Sandberg, Rickard, 2005. "Dickey-Fuller Type of Tests against Nonlinear Dynamic Models," SSE/EFI Working Paper Series in Economics and Finance 580, Stockholm School of Economics.
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    1. Lunde, Asger & Sandberg, Rickard & Söderberg, Magnus, 2019. "Calculating the damage of a cartel subject to transition periods: The international uranium cartel in the 1970s," Energy Economics, Elsevier, vol. 84(C).
    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.
    3. Rickard Sandberg, 2016. "Testing for unit roots in nonlinear heterogeneous panels with smoothly changing trends: an application to Scandinavian unemployment rates," Empirical Economics, Springer, vol. 51(3), pages 1053-1083, November.
    4. Anoop Chaturvedi & Shivam Jaiswal, 2020. "Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(4), pages 733-745, December.
    5. Li, Dao & He, Changli, 2012. "Testing Common Nonlinear Features in Nonlinear Vector Autoregressive Models," Working Papers 2012:7, Örebro University, School of Business.

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