A Flexible Coefficient Smooth Transition Time Series Model
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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|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.|
|Contact details of provider:|| Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden|
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
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- Dijk, Dick van & Franses, Philip Hans, 1999.
"Modeling Multiple Regimes in the Business Cycle,"
Cambridge University Press, vol. 3(03), pages 311-340, September.
- Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999.
"A simple variable selection technique for nonlinear models,"
SFB 373 Discussion Papers
1999,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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.
- Eitrheim, Oyvind & Terasvirta, Timo, 1996.
"Testing the adequacy of smooth transition autoregressive models,"
Journal of Econometrics,
Elsevier, vol. 74(1), pages 59-75, September.
- Eitrheim, Øyvind & Teräsvirta, Timo, 1995. "Testing the Adequacy of Smooth Transition Autoregressive Models," SSE/EFI Working Paper Series in Economics and Finance 56, Stockholm School of Economics.
- 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.
- 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.
- Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207, December.
- 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.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, December.
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