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Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors

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Abstract

In this paper, we discuss tests of heteroscedasticity and/or autocorrelation in nonlinear models with AR(1) and symmetrical errors. The symmetrical errors distribution class includes all symmetrical continuous distributions, such as normal, Student-t, power exponential, logistic I and II, contaminated normal, so on. First, score test statistics and their adjustment forms of heteroscedasticity are derived. Then, the asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied. The properties of test statistics are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our test methods.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Chun-Zheng Cao & Jin-Guan Lin

  2. College of Math and Physics, University of Information Science and Technology, 210044, Nanjing, China

    Chun-Zheng Cao

  3. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

    Li-Xing Zhu

Authors
  1. Chun-Zheng Cao
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  2. Jin-Guan Lin
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  3. Li-Xing Zhu
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Corresponding author

Correspondence to Jin-Guan Lin.

Additional information

The project was supported by NSFC (10671032), NSF,JS (BK2008284), and a grant (HKBU2030/07P) from the Grant Council of Hong Kong, Hong Kong, China.

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Cao, CZ., Lin, JG. & Zhu, LX. Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors. Stat Papers 51, 813–836 (2010). https://doi.org/10.1007/s00362-008-0171-y

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  • DOI: https://doi.org/10.1007/s00362-008-0171-y

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