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Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models

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  • Hong, Yongmiao
  • Lee, Tae-Hwy
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    Abstract

    We propose a new diagnostic test for linear and nonlinear time series models, using a generalized spectral approach. Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing nuisance-parameter-free property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic. It is consistent against any type of pairwise serial dependence in the model standardized residuals and allows the choice of a proper lag order via data-driven methods. Moreover, the new test is asymptotically more efficient than the correlation integral based test of Brock, Hsieh, and LeBaron (1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence) and Brock, Dechert, Scheinkman, and LeBaron (1996, Econometric Reviews 15, 197 235), the well-known BDS test, against a class of plausible local alternatives (not including ARCH). A simulation study compares the finite-sample performance of the proposed test and the tests of BDS, Box and Pierce (1970, Journal of the American Statistical Association 65, 1509 1527), Ljung and Box (1978, Biometrika 65, 297 303), McLeod and Li (1983, Journal of Time Series Analysis 4, 269 273), and Li and Mak (1994, Journal of Time Series Analysis 15, 627 636). The new test has good power against a wide variety of stochastic and chaotic alternatives to the null models for conditional mean and conditional variance. It can play a valuable role in evaluating adequacy of linear and nonlinear time series models. An empirical application to the daily S P 500 price index highlights the merits of our approach.We thank the co-editor (Don Andrews) and two referees for careful and constructive comments that have lead to significant improvement over an earlier version. We also thank C.W.J. Granger, D. Tj stheim, and Z. Xiao for helpful comments. Hong s participation is supported by the National Science Foundation via NSF grant SES 0111769. Lee thanks the UCR Academic Senate for research support.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 19 (2003)
    Issue (Month): 06 (December)
    Pages: 1065-1121

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    Handle: RePEc:cup:etheor:v:19:y:2003:i:06:p:1065-1121_19

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    Cited by:
    1. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, 09.
    2. Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra.
    3. repec:wyi:journl:002087 is not listed on IDEAS
    4. Philippe Lambert & Sébastien Laurent, 2008. "Testing Conditional Dynamics in Asymmetry. A Residual-Based Approach," Working Papers ECARES 2008_009, ULB -- Universite Libre de Bruxelles.
    5. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1229-1247.
    6. Yi-Ting Chen, 2008. "A unified approach to standardized-residuals-based correlation tests for GARCH-type models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 111-133.
    7. Gloria González-Rivera & Tae-Hwy Lee & Santosh Mishra, 2008. "Jumps in cross-sectional rank and expected returns: a mixture model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 585-606.
    8. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    9. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
    10. repec:wyi:journl:002120 is not listed on IDEAS
    11. repec:wyi:journl:002062 is not listed on IDEAS
    12. Meitz, Mika & Teräsvirta, Timo, 2004. "Evaluating models of autoregressive conditional duration," Working Paper Series in Economics and Finance 557, Stockholm School of Economics, revised 13 Dec 2004.
    13. Patrick W Saart & Jiti Gao & Nam Hyun Kim, 2014. "Econometric Time Series Specification Testing in a Class of Multiplicative Error Models," Monash Econometrics and Business Statistics Working Papers 1/14, Monash University, Department of Econometrics and Business Statistics.
    14. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    15. Gloria González-Rivera & Tae-Hwy Lee, 2007. "Nonlinear Time Series in Financial Forecasting," Working Papers 200803, University of California at Riverside, Department of Economics, revised Feb 2008.
    16. Chen, Min & Zhu, Ke, 2013. "Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations," MPRA Paper 50487, University Library of Munich, Germany.

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