IDEAS home Printed from https://ideas.repec.org/p/aah/create/2010-01.html
   My bibliography  Save this paper

Forecasting with nonlinear time series models

Author

Listed:
  • Anders Bredahl Kock

    () (CREATES, Aarhus University)

  • Timo Teräsvirta

    () (CREATES, Aarhus University)

Abstract

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econometrics are presented and some of their properties discussed. This includes two models based on universal approximators: the Kolmogorov-Gabor polynomial model and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with complex dynamic systems, albeit less frequently applied to economic forecasting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a particular case where the data-generating process is a simple artificial neural network model. Suggestions for further reading conclude the paper.

Suggested Citation

  • Anders Bredahl Kock & Timo Teräsvirta, 2010. "Forecasting with nonlinear time series models," CREATES Research Papers 2010-01, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-01
    as

    Download full text from publisher

    File URL: ftp://ftp.econ.au.dk/creates/rp/10/rp10_01.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. González Andrés & Teräsvirta Timo, 2008. "Modelling Autoregressive Processes with a Shifting Mean," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-28, March.
    2. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, Fall.
    3. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    4. 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.
    5. Maximo Camacho, 2004. "Vector smooth transition regression models for US GDP and the composite index of leading indicators," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(3), pages 173-196.
    6. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
    7. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    8. Krolzig, Hans-Martin & Hendry, David F., 2001. "Computer automation of general-to-specific model selection procedures," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 831-866, June.
    9. Kock Anders Bredahl, 2011. "Forecasting with Universal Approximators and a Learning Algorithm," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    10. Marcellino, Massimliano, 2004. "Forecasting EMU macroeconomic variables," International Journal of Forecasting, Elsevier, vol. 20(2), pages 359-372.
    11. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    12. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    13. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    14. Bajo-Rubio, Oscar & Sosvilla-Rivero, Simon & Fernandez-Rodriguez, Fernando, 2001. "Asymmetry in the EMS: New evidence based on non-linear forecasts," European Economic Review, Elsevier, vol. 45(3), pages 451-473, March.
    15. Norman R. Swanson & Halbert White, 1997. "A Model Selection Approach To Real-Time Macroeconomic Forecasting Using Linear Models And Artificial Neural Networks," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 540-550, November.
    16. Massimiliano Marcellino, "undated". "Instability and non-linearity in the EMU," Working Papers 211, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, Elsevier.
    18. Rech, Gianluigi, 2002. "Forecasting with artificial neural network models," SSE/EFI Working Paper Series in Economics and Finance 491, Stockholm School of Economics.
    19. Swanson, Norman R. & White, Halbert, 1997. "Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models," International Journal of Forecasting, Elsevier, vol. 13(4), pages 439-461, December.
    20. Lanne, Markku & Saikkonen, Pentti, 2002. "Threshold Autoregressions for Strongly Autocorrelated Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 282-289, April.
    21. Maravall, Agustin, 1983. "An Application of Nonlinear Time Series Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 66-74, January.
    22. 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.
    23. Jaditz, Ted & Riddick, Leigh A. & Sayers, Chera L., 1998. "MULTIVARIATE NONLINEAR FORECASTING Using Financial Information to Forecast the Real Sector," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 369-382, September.
    24. Kuan, Chung-Ming & Liu, Tung, 1995. "Forecasting Exchange Rates Using Feedforward and Recurrent Neural Networks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 347-364, Oct.-Dec..
    25. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier.
    26. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    27. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    28. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, vol. 158(2), pages 231-245, October.
    29. Jurgen A. Doornik, 2008. "Encompassing and Automatic Model Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 915-925, December.
    30. 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.
    31. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895, November.
    32. White, Halbert, 2006. "Approximate Nonlinear Forecasting Methods," Handbook of Economic Forecasting, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kock, Anders Bredahl & Teräsvirta, Timo, 2014. "Forecasting performances of three automated modelling techniques during the economic crisis 2007–2009," International Journal of Forecasting, Elsevier, vol. 30(3), pages 616-631.
    2. Jennifer Castle & David Hendry, 2013. "Semi-automatic Non-linear Model selection," Economics Series Working Papers 654, University of Oxford, Department of Economics.
    3. Oscar Claveria & Enric Monte & Salvador Torra, 2015. "“Self-organizing map analysis of agents’ expectations. Different patterns of anticipation of the 2008 financial crisis”," AQR Working Papers 201508, University of Barcelona, Regional Quantitative Analysis Group, revised Mar 2015.
    4. Oscar Claveria & Salvador Torra, 2013. "“Forecasting Business surveys indicators: neural networks vs. time series models”," IREA Working Papers 201320, University of Barcelona, Research Institute of Applied Economics, revised Nov 2013.
    5. Anders Bredahl Kock & Timo Teräsvirta, 2016. "Forecasting Macroeconomic Variables Using Neural Network Models and Three Automated Model Selection Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1753-1779, December.
    6. Hayashi, Masayoshi, 2014. "Forecasting welfare caseloads: The case of the Japanese public assistance program," Socio-Economic Planning Sciences, Elsevier, vol. 48(2), pages 105-114.
    7. Meriam BouAli & Adnen Ben Nasr & Abdelwahed Trabelsi, 2016. "A Nonlinear Approach for Modeling and Forecasting US Business Cycles," International Economic Journal, Taylor & Francis Journals, vol. 30(1), pages 39-74, March.
    8. Ramazan Gencay & Ege Yazgan, 2017. "When Are Wavelets Useful Forecasters?," Working Papers 1704, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    9. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    10. Shahid IQBAL & Maqbool H. SIAL, 2016. "Projections of Inflation Dynamics for Pakistan: GMDH Approach," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 536-559, September.
    11. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2012. "Is there an optimal forecast combination? A stochastic dominance approach applied to the forecast combination puzzle," Working Papers 1206, University of Guelph, Department of Economics and Finance.
    12. Souhaib Ben Taieb & Rob J Hyndman, 2014. "Boosting multi-step autoregressive forecasts," Monash Econometrics and Business Statistics Working Papers 13/14, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    forecast accuracy; Kolmogorov-Gabor; nearest neighbour; neural network; nonlinear regression;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2010-01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.econ.au.dk/afn/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.