FIRST-ORDER ASYMPTOTIC THEORY FOR PARAMETRIC MISSPECIFICATION TESTS OF GARCH MODELS
基于一阶渐近理论，构建了GARCH模型参数误设检验框架，发现条件均值函数正确设定带来的估计效应在渐近上不可忽略，导致Engle和Ng（1993）的非对称性检验及Lundbergh和Teräsvirta（2002）的非线性检验渐近无效，并提出具有更优功效的替代检验方法。
This paper develops a framework for the construction and analysis of parametric misspecification tests for generalized autoregressive conditional heteroskedastic (GARCH) models, based on first-order asymptotic theory. The principal finding is that estimation effects from the correct specification of the conditional mean (regression) function can be asymptotically nonnegligible. This implies that certain procedures, such as the asymmetry tests of Engle and Ng (1993, Journal of Finance 48, 1749–1777) and the nonlinearity test of Lundbergh and Teräsvirta (2002, Journal of Econometrics 110, 417–435), are asymptotically invalid. A second contribution is the proposed use of alternative tests for asymmetry and/or nonlinearity that, it is conjectured, should enjoy improved power properties. A Monte Carlo study supports the principal theoretical findings and also suggests that the new tests have fairly good size and very good power properties when compared with the Engle and Ng (1993) and Lundbergh and Teräsvirta (2002) procedures.