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A Flexible Coefficient Smooth Transition Time Series Model

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 360.

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Length: 40 pages
Date of creation: 09 Feb 2000
Date of revision: 10 Feb 2000
Publication status: Published in IEEE Transactions on Neural Networks, 2005, pages 97-113.
Handle: RePEc:hhs:hastef:0360

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

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References

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  1. Eitrheim, Øyvind & Teräsvirta, Timo, 1995. "Testing the Adequacy of Smooth Transition Autoregressive Models," Working Paper Series in Economics and Finance 56, Stockholm School of Economics.
  2. 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.
  3. 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.
  4. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," Working Paper Series in Economics and Finance 296, Stockholm School of Economics, revised 06 Apr 2000.
  5. repec:wop:humbsf:1999-26 is not listed on IDEAS
  6. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207, September.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
  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. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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).
  4. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. Lof, Matthijs, 2010. "Heterogeneity in Stock Pricing: A STAR Model with Multivariate Transition Functions," MPRA Paper 30520, University Library of Munich, Germany.
  6. 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, 07.
  7. 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).
  8. 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).
  9. Leila Ali & Marie Lebreton, 2013. "The Fall of Bretton Woods: Which Geography Matters?," Economics Bulletin, AccessEcon, vol. 33(2), pages 1396-1419.
  10. 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 Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  11. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
  12. Khurshid Kiani & Terry Kastens, 2008. "Testing Forecast Accuracy of Foreign Exchange Rates: Predictions from Feed Forward and Various Recurrent Neural Network Architectures," Computational Economics, Society for Computational Economics, vol. 32(4), pages 383-406, November.
  13. Marie Lebreton & Katia Melnik, 2009. "Voluntary Participation as a Determinant of Social Capital in France : Allowing for Parameter Heterogeneity," Working Papers halshs-00410530, HAL.
  14. 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).

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