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Stationarity and ergodicity of vector STAR models

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  • Igor L. Kheifets
  • Pentti J. Saikkonen

Abstract

Smooth transition autoregressive models are widely used to capture nonlinearities in univariate and multivariate time series. Existence of stationary solution is typically assumed, implicitly or explicitly. In this paper we describe conditions for stationarity and ergodicity of vector STAR models. The key condition is that the joint spectral radius of certain matrices is below 1, which is not guaranteed if only separate spectral radii are below 1. Our result allows to use recently introduced toolboxes from computational mathematics to verify the stationarity and ergodicity of vector STAR models.

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  • Igor L. Kheifets & Pentti J. Saikkonen, 2018. "Stationarity and ergodicity of vector STAR models," Papers 1805.11311, arXiv.org, revised Aug 2019.
    • Handle: RePEc:arx:papers:1805.11311
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    References listed on IDEAS

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    1. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
    2. George Athanasopoulos & Heather M. Anderson & Farshid Vahid, 2007. "Nonlinear autoregressive leading indicator models of output in G-7 countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 63-87.
    3. Kheifets, Igor L., 2018. "Multivariate specification tests based on a dynamic Rosenblatt transform," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 1-14.
    4. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    5. BLONDEL, Vincent D. & NESTEROV, Yu., 2005. "Computationally efficient approximations of the joint spectral radius," LIDAM Reprints CORE 1800, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
    7. Saikkonen, Pentti, 2008. "Stability Of Regime Switching Error Correction Models Under Linear Cointegration," Econometric Theory, Cambridge University Press, vol. 24(1), pages 294-318, February.
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    Cited by:

    1. Bucci, Andrea & Sanmarchi, Francesco & Santi, Luca & Golinelli, Davide, 2024. "Evaluating the nonlinear association between PM10 and emergency department visits," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    2. James A. Duffy & Sophocles Mavroeidis & Sam Wycherley, 2022. "Cointegration with Occasionally Binding Constraints," Papers 2211.09604, arXiv.org, revised Jul 2023.
    3. Andrea Bucci, 2024. "A sequential test procedure for the choice of the number of regimes in multivariate nonlinear models," Papers 2406.02152, arXiv.org.

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