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Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models

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  • Daniel Buncic

Abstract

Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill‐suited as a regime weighting function because of two undesirable properties. Firstly, it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is ‘small’. This leads to an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of γ. This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter μ. We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise.

Suggested Citation

  • Daniel Buncic, 2019. "Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 667-685, June.
    • Handle: RePEc:bla:obuest:v:81:y:2019:i:3:p:667-685
    DOI: 10.1111/obes.12264
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    1. He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2021. "Comparing long monthly Chinese and selected European temperature series using the Vector Seasonal Shifting Mean and Covariance Autoregressive model," Energy Economics, Elsevier, vol. 97(C).
    2. He, Changli & Kang, Jian & Silvennoinen, Annastiina & Teräsvirta, Timo, 2024. "Long monthly temperature series and the Vector Seasonal Shifting Mean and Covariance Autoregressive model," Journal of Econometrics, Elsevier, vol. 239(1).
    3. Selin Güney & Andrés Riquelme & Barry Goodwin, 2023. "An Analysis of the Pass-Through of Exchange Rates in Forest Product Markets," Agriculture, MDPI, vol. 13(3), pages 1-16, February.
    4. Esmaeil Ebadi & Yousef Abdul Razaq, 2024. "Reinvestigating the Oil Dependency of the GCC Countries’ Stock Market: A Regime-Switching Cointegration Approach," International Journal of Energy Economics and Policy, Econjournals, vol. 14(3), pages 387-406, May.
    5. Elias, Nikolaos & Smyrnakis, Dimitris & Tzavalis, Elias, 2024. "The forward premium anomaly and the currency carry trade hypothesis," The Quarterly Review of Economics and Finance, Elsevier, vol. 95(C), pages 203-218.
    6. Anoop Chaturvedi & Shivam Jaiswal, 2020. "Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(4), pages 733-745, December.
    7. Dimitris Christopoulos & Peter McAdam & Elias Tzavalis, 2023. "Exploring Okun's law asymmetry: An endogenous threshold logistic smooth transition regression approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(1), pages 123-158, February.
    8. He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2019. "The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016," Econometrics and Statistics, Elsevier, vol. 12(C), pages 1-24.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • F30 - International Economics - - International Finance - - - General
    • F44 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Business Cycles

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