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Local Unit Roots and Global Stationarity of TARMA Models

Author

Listed:
  • Marcella Niglio

    (University of Salerno
    University of Salerno)

  • Cosimo Damiano Vitale

    (University of Salerno)

Abstract

In this paper the (strict and weak) stationarity of threshold autoregressive moving average models is discussed. After examining the strict stationarity, mainly based on the random coefficient autoregressive representation of the model, we provide sufficient conditions for its weak stationarity that allow to obtain a wider stationarity region with respect to some previous results given in the literature. These conditions are discussed to distinguish between global and local stationarity, whose relation has been considered in detail. The threshold process has been further evaluated to face the problem related to the so called existence of a threshold structure in the data generating process that is strictly related to the stationarity and has significant relevance when the parameters of the model have to be estimated.

Suggested Citation

  • Marcella Niglio & Cosimo Damiano Vitale, 2012. "Local Unit Roots and Global Stationarity of TARMA Models," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 17-34, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9166-y
    DOI: 10.1007/s11009-010-9166-y
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    References listed on IDEAS

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    1. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
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    3. Stelzer, Robert, 2009. "On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity," Econometric Theory, Cambridge University Press, vol. 25(1), pages 43-62, February.
    4. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    5. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
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