Bruce E. Hansen

"Testing for Linearity", Journal of Economic Surveys, (1999), 13, 551-576.


The problem of testing for linearity and the number of regimes in the context of self-exciting threshold autoregressive (SETAR) models is reviewed. We describe least-squares methods of estimation and inference. The primary complication is that the testing problem is non-standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non-standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented.

As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications -- annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes.

The copyright to this article is held by the the Journal of Economic Surveys. It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for-profit commercial firm or other commercial purpose.

Download PDF file (648 KB)

Link to Programs and Data

Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.