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A Flexible Coefficient Smooth Transition Time Series Model

Author

Listed:
  • Medeiros, Marcelo

    () (Dept. of Economic Statistics, Stockholm School of Economics)

  • Veiga, Alvaro

    () (Dept. of Electrical Engineering, Catholic University of Rio de Janeiro (PUC-Rio))

Abstract

In this paper, we propose a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. We show that this formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the Self-Exciting Threshold AutoRegressive (SETAR), the AutoRegressive Artificial Neural Network (AR-ANN), and the Logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel-measurable function, our formulation is directly comparable to the Functional Coefficient AutoRegressive (FAR) and the Single-Index Coefficient Regression models. The motivation for developing a flexible model is twofold. First, allowing for multiple regimes is important to model the dynamics of several time series, as for example, the behaviour of macro economic variables over the business cycle. Second, multiple transition variables are useful in describing complex nonlinear behaviour and allow for different sources of nonlinearity. A model building procedure consisting of specification and estimation is developed based on statistical inference arguments. A Monte-Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.

Suggested Citation

  • Medeiros, Marcelo & Veiga, Alvaro, 2000. "A Flexible Coefficient Smooth Transition Time Series Model," SSE/EFI Working Paper Series in Economics and Finance 360, Stockholm School of Economics, revised 29 Apr 2004.
  • Handle: RePEc:hhs:hastef:0360
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    References listed on IDEAS

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    1. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    2. Yao, Qiwei & Tong, Howell, 1994. "On subset selection in non-parametric stochastic regression," LSE Research Online Documents on Economics 6409, London School of Economics and Political Science, LSE Library.
    3. Cooper, Suzanne J, 1998. "Multiple Regimes in U.S. Output Fluctuations," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 92-100, January.
    4. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," SSE/EFI Working Paper Series in Economics and Finance 296, Stockholm School of Economics, revised 06 Apr 2000.
    5. Astatkie, T. & Watts, D. G. & Watt, W. E., 1997. "Nested threshold autoregressive (NeTAR) models," International Journal of Forecasting, Elsevier, vol. 13(1), pages 105-116, March.
    6. Dijk, Dick van & Franses, Philip Hans, 1999. "Modeling Multiple Regimes in the Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 3(03), pages 311-340, September.
    7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    8. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    9. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
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    Citations

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    Cited by:

    1. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    2. Marcelo C. Medeiros & Alvaro Veiga, 2003. "Diagnostic Checking in a Flexible Nonlinear Time Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 461-482, July.
    3. Marcelo Cunha Medeiros & Álvaro Veiga & Carlos Eduardo Pedreira, 2000. "Modelling exchange rates: smooth transitions, neural networks, and linear models," Textos para discussão 432, Department of Economics PUC-Rio (Brazil).
    4. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
    5. Marie Lebreton & Katia Melnik, 2009. "Voluntary Participation as a Determinant of Social Capital in France : Allowing for Parameter Heterogeneity," Working Papers halshs-00410530, HAL.
    6. Eduardo Mendes & Alvaro Veiga & MArcelo Cunha Medeiros, 2007. "Estimation And Asymptotic Theory For A New Class Of Mixture Models," Textos para discussão 538, Department of Economics PUC-Rio (Brazil).
    7. Areosa, Waldyr Dutra & McAleer, Michael & Medeiros, Marcelo C., 2011. "Moment-based estimation of smooth transition regression models with endogenous variables," Journal of Econometrics, Elsevier, vol. 165(1), pages 100-111.
    8. Khurshid Kiani & Terry Kastens, 2008. "Testing Forecast Accuracy of Foreign Exchange Rates: Predictions from Feed Forward and Various Recurrent Neural Network Architectures," Computational Economics, Springer;Society for Computational Economics, vol. 32(4), pages 383-406, November.
    9. Marcelo Cunha Medeiros & Alvaro Veiga, 2004. "Modelling multiple regimes in financial volatility with a flexible coefficient GARCH model," Textos para discussão 486, Department of Economics PUC-Rio (Brazil).
    10. Lebreton, Marie, 2005. "The NCSTAR model as an alternative to the GWR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 77-84.
    11. José Luis Aznarte & Marcelo Cunha Medeiros & José Manuel Benítez Sánchez, 2010. "Linearity Testing Against a Fuzzy Rule-based Model," Textos para discussão 566, Department of Economics PUC-Rio (Brazil).
    12. Lof, Matthijs, 2010. "Heterogeneity in Stock Pricing: A STAR Model with Multivariate Transition Functions," MPRA Paper 30520, University Library of Munich, Germany.
    13. Leila Ali & Marie Lebreton, 2013. "The Fall of Bretton Woods: Which Geography Matters?," Economics Bulletin, AccessEcon, vol. 33(2), pages 1396-1419.
    14. da Rosa, Joel Correa & Veiga, Alvaro & Medeiros, Marcelo C., 2008. "Tree-structured smooth transition regression models," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2469-2488, January.
    15. João Paulo Martin Faleiros & Denisard Cnéio de Oliveira Alves, 2008. "Modelo de Crescimento Baseado nas Exportações: Evidências empíricas para Chile, Brasil e México, em uma perspectiva Não Linear," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807170923500, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].

    More about this item

    Keywords

    Time series; smooth transition models; threshold models; neural networks;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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