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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. It is not sufficient to assume that 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.

Suggested Citation

  • Igor L. Kheifets & Pentti J. Saikkonen, 2020. "Stationarity and ergodicity of vector STAR models," Econometric Reviews, Taylor & Francis Journals, vol. 39(4), pages 407-414, April.
    • Handle: RePEc:taf:emetrv:v:39:y:2020:i:4:p:407-414
    DOI: 10.1080/07474938.2019.1651489
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    Cited by:

    1. Lanne, Markku & Virolainen, Savi, 2025. "A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 178(C).
    2. Andrea Bucci, 2024. "A sequential test procedure for the choice of the number of regimes in multivariate nonlinear models," Papers 2406.02152, arXiv.org.
    3. Chen, Pu & Semmler, Willi & Maurer, Helmut, 2025. "Delayed Monetary Policy Effects in a Multi-Regime Cointegrated VAR(MRCIVAR)," Econometrics and Statistics, Elsevier, vol. 33(C), pages 105-134.
    4. Duffy, James A. & Mavroeidis, Sophocles & Wycherley, Sam, 2025. "Cointegration with occasionally binding constraints," Journal of Econometrics, Elsevier, vol. 252(PA).
    5. Andrea Bucci, 2025. "Correction to: A Smooth Transition Autoregressive Model for Matrix-Variate Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 65(1), pages 459-462, January.
    6. 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).

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