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A Diagnostic Test For Nonlinear Serial Dependence In Time Series Fitting Errors

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  • Richard A. Ashley
  • Douglas M. Patterson
  • Melvin J. Hinich

Abstract

. Time series analysts have begun to consider the applicability of nonlinear models. In order for nonlinear models to be accepted by practitioners, practicai tests must be avilable to test for the presence of nonlinearity in both raw time series and in the residuals from fitted models. A diagnostic test, based on the bispectrum, for the presence of nonlinear serial dependence in these time series is investigated here using artificial data. Detection of such nonlinear dependence is taken to indicate that nonlinear modelling methods are necessary. The theory behind the test is reviewed and simulations driven by pseudorandom numbers are presented for a variety of models and sample sizes. The simulations indicate that the test has substantial power for many models. In addition, theoretical and empirical results are presented which show that the bispectral diagnostic test is equally powerful for both the source series and for the fitting errors from a line& model. Thus, while the test is suitable for use as a diagnostic test on the fitting errors of linear time series models, prior linear modeling of the time series is not required.

Suggested Citation

  • Richard A. Ashley & Douglas M. Patterson & Melvin J. Hinich, 1986. "A Diagnostic Test For Nonlinear Serial Dependence In Time Series Fitting Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 165-178, May.
    • Handle: RePEc:bla:jtsera:v:7:y:1986:i:3:p:165-178
    DOI: 10.1111/j.1467-9892.1986.tb00500.x
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    Cited by:

    1. Nesmith Travis D & Jones Barry E, 2008. "Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-18, March.
    2. Ammermann, Peter A. & Patterson, Douglas M., 2003. "The cross-sectional and cross-temporal universality of nonlinear serial dependencies: Evidence from world stock indices and the Taiwan Stock Exchange," Pacific-Basin Finance Journal, Elsevier, vol. 11(2), pages 175-195, April.
    3. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    4. Mills, Terence C., 1995. "Business cycle asymmetries and non-linearities in U.K. macroeconomic time series," Ricerche Economiche, Elsevier, vol. 49(2), pages 97-124, June.
    5. William A. Barnett & Melvin J. Hinich & Piyu Yue, 2011. "The Exact Theoretical Rational Expectations Monetary Aggregate," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, chapter 2, pages 53-84, World Scientific Publishing Co. Pte. Ltd..
    6. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    7. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
    8. Harvill, Jane L. & Ravishanker, Nalini & Ray, Bonnie K., 2013. "Bispectral-based methods for clustering time series," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 113-131.
    9. Kian-Ping Lim & M. Azali & M.S. Habibullah & Venus Khim-Sen Liew, 2003. "Are Non-Linear Dynamics a Universal Occurrence? Further Evidence From Asian Stock Markets," Finance 0308001, University Library of Munich, Germany.
    10. T Tang, 2009. "Testing for Non-linearity in the Balancing Item of Balance of Payments Accounts: The Case of 20 Industrial Countries," Economic Issues Journal Articles, Economic Issues, vol. 14(2), pages 107-124, September.
    11. Wild, Phillip & Hinich, Melvin J. & Foster, John, 2010. "Are daily and weekly load and spot price dynamics in Australia's National Electricity Market governed by episodic nonlinearity?," Energy Economics, Elsevier, vol. 32(5), pages 1082-1091, September.
    12. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    13. Jane L. Harvill & Priya Kohli & Nalini Ravishanker, 2017. "Clustering Nonlinear, Nonstationary Time Series Using BSLEX," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 935-955, September.
    14. Dahl, Christian M. & Gonzalez-Rivera, Gloria, 2003. "Testing for neglected nonlinearity in regression models based on the theory of random fields," Journal of Econometrics, Elsevier, vol. 114(1), pages 141-164, May.
    15. Phillip Wild & John Foster, 2012. "On testing for non-linear and time irreversible probabilistic structure in high frequency ASX financial time series data," Discussion Papers Series 466, School of Economics, University of Queensland, Australia.
    16. Teles, Paulo & Wei, William W. S., 2000. "The effects of temporal aggregation on tests of linearity of a time series," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 91-103, July.
    17. Ahn, Eun S. & Lee, Jin Man, 2012. "The Performance Of Nonlinearity Tests On Asymmetric Nonlinear Time Series," The Journal of Economic Asymmetries, Elsevier, vol. 9(2), pages 11-44.
    18. Adrian G Barnett & Rodney Wolff, 2003. "A Time-Domain Test for Some Types of Non-Linearity," School of Economics and Finance Discussion Papers and Working Papers Series 168, School of Economics and Finance, Queensland University of Technology.
    19. William Barnett & Barry E. Jones & Milka Kirova & Travis D. Nesmith & Meenakshi Pasupathy1, 2004. "The Nonlinear Skeletons in the Closet," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200403, University of Kansas, Department of Economics, revised May 2004.
    20. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
    21. Philip Rothman, "undated". "Higher-Order Residual Analysis for Simple Bilinear and Threshold Autoregressive Models with the TR Test," Working Papers 9813, East Carolina University, Department of Economics.
    22. Hinich Melvin J & Mendes Eduardo M & Stone Lewi, 2005. "Detecting Nonlinearity in Time Series: Surrogate and Bootstrap Approaches," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-15, December.
    23. Kian-Ping Lim & Venus Khim-Sen Liew, 2003. "Testing for Non-Linearity in ASEAN Financial Markets," Finance 0308002, University Library of Munich, Germany.
    24. Houston Stokes & Melvin Hinich, 2011. "Detecting and modeling nonlinearity in the gas furnace data," Computational Statistics, Springer, vol. 26(1), pages 77-93, March.
    25. Olmedo, Elena, 2011. "Is there chaos in the Spanish labour market?," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1045-1053.

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