Journal
STATISTICAL PAPERS
Volume 51, Issue 4, Pages 813-836Publisher
SPRINGER
DOI: 10.1007/s00362-008-0171-y
Keywords
Symmetrical distributions; Nonlinear model; AR(1) errors; Heteroscedasticity; Score test; Asymptotic properties; Approximate local powers
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Funding
- NSFC [10671032]
- NSF,JS [BK2008284]
- Grant Council of Hong Kong, Hong Kong, China [HKBU2030/07P]
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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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