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On a robust test for SETAR-type nonlinearity in time series analysis

  • King Chi Hung

    (Chinese University of Hong Kong, Hong Kong)

  • Siu Hung Cheung
  • Wai-Sum Chan

    (Chinese University of Hong Kong, Hong Kong)

  • Li-Xin Zhang

    (Zhejiang University, PR China)

Registered author(s):

    There has been growing interest in exploiting potential forecast gains from the nonlinear structure of self-exciting threshold autoregressive (SETAR) models. Statistical tests have been proposed in the literature to help analysts check for the presence of SETAR-type nonlinearities in observed time series. However, previous studies show that classical nonlinearity tests are not robust to additive outliers. In practice, time series outliers are not uncommonly encountered. It is important to develop a more robust test for SETAR-type nonlinearity in time series analysis and forecasting. In this paper we propose a new robust nonlinearity test and the asymptotic null distribution of the test statistic is derived. A Monte Carlo experiment is carried out to compare the power of the proposed test with other existing tests under the influence of time series outliers. The effects of additive outliers on nonlinearity tests with misspecification of the autoregressive order are also studied. The results indicate that the proposed method is preferable to the classical tests when the observations are contaminated with outliers. Finally, we provide illustrative examples by applying the statistical tests to three real datasets. Copyright © 2009 John Wiley & Sons, Ltd.

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    File URL: http://hdl.handle.net/10.1002/for.1122
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    Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

    Volume (Year): 28 (2009)
    Issue (Month): 5 ()
    Pages: 445-464

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    Handle: RePEc:jof:jforec:v:28:y:2009:i:5:p:445-464
    DOI: 10.1002/for.1122
    Contact details of provider: Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966

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    1. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for Smooth Transition Nonlinearity in the Presence of Outliers," Econometric Institute Research Papers EI 9622-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
    3. De Gooijer, Jan G. & Kumar, Kuldeep, 1992. "Some recent developments in non-linear time series modelling, testing, and forecasting," International Journal of Forecasting, Elsevier, vol. 8(2), pages 135-156, October.
    4. Man-Wai Ng & Wai-Sum Chan, 2004. "Robustness of alternative non-linearity tests for SETAR models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(3), pages 215-231.
    5. Sarantis, Nicholas, 2001. "Nonlinearities, cyclical behaviour and predictability in stock markets: international evidence," International Journal of Forecasting, Elsevier, vol. 17(3), pages 459-482.
    6. Chen, Cathy W. S., 1997. "Detection of additive outliers in bilinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 283-294, May.
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