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A robust Cusum test for SETAR-type nonlinearity in time series


  • Joseph D. Petruccelli

    (Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts, USA)

  • Alina Onofrei

    (Division of Preventive and Behavioral Medicine, University of Massachusetts Medical School, Worcester, Massachusetts, USA)

  • Jayson D. Wilbur

    (Instrumentation Laboratory, Lexington, Massachusetts, 02421, USA)


As a part of an effective self-exciting threshold autoregressive (SETAR) modeling methodology, it is important to identify processes exhibiting SETAR-type nonlinearity. A number of tests of nonlinearity have been developed in the literature. However, it has recently been shown that all these tests perform poorly for SETAR-type nonlinearity detection in the presence of additive outliers. In this paper, we develop an improved test for SETAR-type nonlinearity in time series. The test is an outlier-robust test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits. A Monte Carlo study confirms that the proposed test is competitive with existing tests for data from uncontaminated SETAR models and superior to them for SETAR data contaminated with additive outliers. Copyright © 2008 John Wiley & Sons, Ltd.

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  • Joseph D. Petruccelli & Alina Onofrei & Jayson D. Wilbur, 2009. "A robust Cusum test for SETAR-type nonlinearity in time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 266-276.
  • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:266-276
    DOI: 10.1002/for.1113

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    References listed on IDEAS

    1. Balke, Nathan S & Fomby, Thomas B, 1994. "Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 181-200, April-Jun.
    2. 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.
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    Cited by:

    1. Yoon, Gawon, 2009. "It's all the miners' fault: On the nonlinearity in U.S. unemployment rates," Economic Modelling, Elsevier, vol. 26(6), pages 1449-1454, November.

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