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Linear approximation of the Threshold AutoRegressive model: an application to order estimation

Author

Listed:
  • Francesco Giordano

    (Università degli Studi di Salerno)

  • Marcella Niglio

    (Università degli Studi di Salerno)

  • Cosimo Damiano Vitale

    (Università degli Studi di Salerno)

Abstract

This paper proposes a linear approximation of the nonlinear Threshold AutoRegressive model. It is shown that there is a relation between the autoregressive order of the threshold model and the order of its autoregressive moving average approximation. The main advantage of this approximation can be found in the extension of some theoretical results developed in the linear setting to the nonlinear domain. Among them is proposed a new order estimation procedure for threshold models whose performance is compared, through a Monte Carlo study, to other criteria largely employed in the nonlinear threshold context.

Suggested Citation

  • Francesco Giordano & Marcella Niglio & Cosimo Damiano Vitale, 2023. "Linear approximation of the Threshold AutoRegressive model: an application to order estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 27-56, March.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00638-1
    DOI: 10.1007/s10260-022-00638-1
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    References listed on IDEAS

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    1. Timmermann, Allan, 2000. "Moments of Markov switching models," Journal of Econometrics, Elsevier, vol. 96(1), pages 75-111, May.
    2. C. S. Wong & W. K. Li, 1998. "A note on the corrected Akaike information criterion for threshold autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 113-124, January.
    3. Rinke Saskia & Sibbertsen Philipp, 2016. "Information criteria for nonlinear time series models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(3), pages 325-341, June.
    4. George Kapetanios, 2001. "Model Selection in Threshold Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 733-754, November.
    5. 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.
    6. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    7. Pham, Dinh Tuan, 1985. "Bilinear markovian representation and bilinear models," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 295-306, September.
    8. Anne B. Koehler & Emily S. Murphree, 1988. "A Comparison of the Akaike and Schwarz Criteria for Selecting Model Order," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 187-195, June.
    9. Zacharias Psaradakis & Martin Sola & Fabio Spagnolo & Nicola Spagnolo, 2009. "Selecting nonlinear time series models using information criteria," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 369-394, July.
    10. Emiliano, Paulo C. & Vivanco, Mário J.F. & de Menezes, Fortunato S., 2014. "Information criteria: How do they behave in different models?," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 141-153.
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