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Biometrika 2002 89(1):245-250; doi:10.1093/biomet/89.1.245
© 2002 by Biometrika Trust
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Miscellaneous

A note on testing for nonlinearity with partially observed time series

Henghsiu Tsai1 and K.S. Chan2

1 Institute of Statistical Science, Academia Sinica, Taipei, Taiwan 115, Republic of China htsai{at}stat.sinica.edu.tw 2 Department of Statistics & Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.Akchan{at}stat.uiowa.edu

We have implemented a Lagrange multiplier test for the alternative hypothesis of a nonlinear continuous-time autoregressive model with the instantaneous mean having multiple degrees of nonlinearity. This test is an extension of a Lagrange multiplier test proposed by Tsai & Chan (2000), with the alternative model analogous to the model used in Tsay's (1986) discrete-time work.The performance of the test in the finite-sample case is compared with several existing tests for nonlinearity including Keenan's (1985) test, Petruccelli & Davies' (1986) test, Tsay's (1986, 1989) tests and Tsai & Chan's (2000) test. The comparison is based on simulated data from some linear autoregressive models, self-exciting threshold autoregressive models, bilinear models and the nonlinear continuous-time autoregressive models for which the Lagrange multiplier test is designed. In general, the test is more powerful than all the other tests. The test is further illustrated with the annual sunspot data and the lynx data.

Key Words: Euler scheme; Irregularly sampled data; Kalman filter; Lagrange multiplier test; Stochastic differential equation

Received August 2000. Revised September 2001


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