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Optimal Formulations for Nonlinear Autoregressive Processes

Author

Listed:
  • Francisco Blasques
  • Siem Jan Koopman
  • André Lucas

    (VU University Amsterdam, the Netherlands)

Abstract

We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The resulting time-varying autoregressive model is formulated as a nonlinear autoregressive model and is compared with threshold and smooth-transition autoregressive models. We establish the information theoretic optimality of the score driven nonlinear autoregressive process and the asymptotic theory for maximum likelihood parameter estimation. The performance of our model in extracting the time-varying or the nonlinear dependence for finite samples is studied in a Monte Carlo exercise. In our empirical study we present the in-sample and out-of-sample performances of our model for a weekly time series of unemployment insurance claims.

Suggested Citation

  • Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Optimal Formulations for Nonlinear Autoregressive Processes," Tinbergen Institute Discussion Papers 14-103/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20140103
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    File URL: https://papers.tinbergen.nl/14103.pdf
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    References listed on IDEAS

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    1. Davide Delle Monache & Ivan Petrella, 2014. "Adaptive Models and Heavy Tails," Working Papers 720, Queen Mary University of London, School of Economics and Finance.
    2. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, September.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    4. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Information Theoretic Optimality of Observation Driven Time Series Models," Tinbergen Institute Discussion Papers 14-046/III, Tinbergen Institute.
    5. Anderson, Patricia M. & Meyer, Bruce D., 2000. "The effects of the unemployment insurance payroll tax on wages, employment, claims and denials," Journal of Public Economics, Elsevier, vol. 78(1-2), pages 81-106, October.
    6. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2014. "Maximum Likelihood Estimation for Score-Driven Models," Tinbergen Institute Discussion Papers 14-029/III, Tinbergen Institute, revised 23 Oct 2017.
    7. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1, Juni.
    8. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    9. Todd E. Clark & Michael W. McCracken, 2010. "Averaging forecasts from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 5-29, January.
    10. Meyer, Bruce D, 1995. "Natural and Quasi-experiments in Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 151-161, April.
    11. Hopenhayn, Hugo A & Nicolini, Juan Pablo, 1997. "Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 412-438, April.
    12. William T. Gavin & Kevin L. Kliesen, 2002. "Unemployment insurance claims and economic activity," Review, Federal Reserve Bank of St. Louis, vol. 84(May), pages 15-28.
    13. Ashenfelter, Orley & Ashmore, David & Deschenes, Olivier, 2005. "Do unemployment insurance recipients actively seek work? Evidence from randomized trials in four U.S. States," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 53-75.
    14. Patricia M. Anderson & Bruce D. Meyer, 1997. "Unemployment Insurance Takeup Rates and the After-Tax Value of Benefits," The Quarterly Journal of Economics, Oxford University Press, vol. 112(3), pages 913-937.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    16. Ullah, Aman, 2002. "Uses of entropy and divergence measures for evaluating econometric approximations and inference," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 313-326, March.
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    Citations

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    Cited by:

    1. Delle Monache, Davide & Petrella, Ivan, 2017. "Adaptive models and heavy tails with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 33(2), pages 482-501.
    2. Roman Frydman & Soren Johansen & Anders Rahbek & Morten Tabor, 2017. "The Qualitative Expectations Hypothesis: Model Ambiguity, Consistent Representations of Market Forecasts, and Sentiment," Working Papers Series 59, Institute for New Economic Thinking.
    3. Delle Monache, Davide & Petrella, Ivan & Venditti, Fabrizio, 2019. "Price Dividend Ratio and Long-Run Stock Returns: a Score Driven State Space Model," EMF Research Papers 29, Economic Modelling and Forecasting Group.
    4. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    5. F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models ," Working Papers hal-01377971, HAL.
    6. Mohamed CHIKHI & Claude DIEBOLT & Tapas MISHRA, 2019. "Does Predictive Ability of an Asset Price Rest in 'Memory'? Insights from a New Approach," Working Papers of BETA 2019-43, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. Davide Delle Monache & Ivan Petrella, 2014. "Adaptive Models and Heavy Tails," Working Papers 720, Queen Mary University of London, School of Economics and Finance.
    8. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2016. "Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models," Tinbergen Institute Discussion Papers 16-082/III, Tinbergen Institute.

    More about this item

    Keywords

    Asymptotic theory; Dynamic models; Observation driven time series models; Smooth-transition model; Time-Varying Parameters; Treshold autoregressive model;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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