Structure and Asymptotic Theory for Nonlinear Models with GARCH Errors∗

Nonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the ∗This paper circulated previously as “Structure and Asymptotic Theory for STAR-GARCH(1,1) Models”. The authors wish to thank Thierry Jeantheau, Offer Lieberman, Shiqing Ling, Howell Tong and Alvaro Veiga for insightful discussions. The first author acknowledges the financial support of the Australian Research Council, the second author is most grateful for the financial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science, and the third author wishes to thank CNPq/Brazil for partial financial support.