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An empirical study on the parsimony and descriptive power of TARMA models

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  • Greta Goracci

    (Universitá di Bologna)

Abstract

In linear time series analysis, the incorporation of the moving-average term in autoregressive models yields parsimony while retaining flexibility; in particular, the first order autoregressive moving-average model, ARMA(1,1) is notable since it retains a good approximating capability with just two parameters. In the same spirit, we assess empirically whether a similar result holds for threshold processes. First, we show that the first order threshold autoregressive moving-average process, TARMA(1,1) exhibits complex, high-dimensional, behaviour with parsimony, by comparing it with threshold autoregressive processes, TAR(p), with possibly large autoregressive order p. Second, we study the descriptive power of the TARMA(1,1) model with respect to the class of autoregressive models, seen as universal approximators: in several situations, the TARMA(1,1) model outperforms AR(p) models even when p is large. Lastly, we analyze two real world data sets: the sunspot number and the male US unemployment rate time series. In both cases, we show that TARMA models provide a better fit with respect to the best TAR models proposed in literature.

Suggested Citation

  • Greta Goracci, 2021. "An empirical study on the parsimony and descriptive power of TARMA models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 109-137, March.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00516-8
    DOI: 10.1007/s10260-020-00516-8
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    References listed on IDEAS

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    1. 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.
    2. Peter J. Brockwell & Jian Liu & Richard L. Tweedie, 1992. "On The Existence Of Stationary Threshold Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 95-107, March.
    3. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    4. Kung‐Sik Chan & Greta Goracci, 2019. "On the Ergodicity of First‐Order Threshold Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(2), pages 256-264, March.
    5. D. K. Ghaddar & H. Tong, 1981. "Data Transformation and Self‐Exciting Threshold Autoregression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(3), pages 238-248, November.
    6. 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.
    7. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.
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