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Local-global neural networks: a new approach for nonlinear time series modelling

Author

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  • Mayte Suarez Farinãs
  • Carlos Eduardo Pedreira
  • Marcelo C. Medeiros

    (Department of Economics PUC-Rio)

Abstract

In this paper, the Local Global Neural Networks model is proposed within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the Mixture of Experts approach. We place emphasis on the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. A model building strategy is also considered and the whole procedure is illustrated with two real time-series.

Suggested Citation

  • Mayte Suarez Farinãs & Carlos Eduardo Pedreira & Marcelo C. Medeiros, 2003. "Local-global neural networks: a new approach for nonlinear time series modelling," Textos para discussão 470, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:470
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    5. 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.
    6. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
    7. Heiler, Siegfried, 1999. "A Survey on Nonparametric Time Series Analysis," CoFE Discussion Papers 99/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    8. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
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    10. Lai T.L. & Po-Shing Wong S., 2001. "Stochastic Neural Networks With Applications to Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 968-981, September.
    11. Swanson, Norman R & White, Halbert, 1995. "A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 265-275, July.
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    Citations

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    Cited by:

    1. 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.
    2. Stockis, Jean-Pierre & Tadjuidje-Kamgaing, Joseph & Franke, Jürgen, 2008. "A note on the identifiability of the conditional expectation for the mixtures of neural networks," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 739-742, April.
    3. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    4. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    5. Medeiros, Marcelo C & Magri, Rafael, 2013. "Nonlinear Error Correction Models With an Application to Commodity Prices," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    6. Marcelo Cunha Medeiros & Felix Chan & Michael McAller, 2005. "Structure and asymptotic theory for STAR(1)-GARCH(1,1) models," Textos para discussão 506, Department of Economics PUC-Rio (Brazil).
    7. McAleer, Michael & Medeiros, Marcelo C. & Slottje, Daniel, 2008. "A neural network demand system with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 147(2), pages 359-371, December.
    8. Medeiros, Marcelo C. & McAleer, Michael & Slottje, Daniel & Ramos, Vicente & Rey-Maquieira, Javier, 2008. "An alternative approach to estimating demand: Neural network regression with conditional volatility for high frequency air passenger arrivals," Journal of Econometrics, Elsevier, vol. 147(2), pages 372-383, December.
    9. 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).
    10. Marcelo Fernandes & Marcelo Cunha Medeiros & Alvaro Veiga, 2006. "A (semi-)parametric functional coefficient autoregressive conditional duration model," Textos para discussão 535, Department of Economics PUC-Rio (Brazil).
    11. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    12. Hillebrand Eric & Medeiros Marcelo C. & Xu Junyue, 2013. "Asymptotic Theory for Regressions with Smoothly Changing Parameters," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 133-162, April.

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    More about this item

    Keywords

    neural networks; nonlinear models; time-series; model identifiability; parameter estimation; model building; sunspot number.;
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