一个新的稳健ARCH检验和YJ-GARCH模型

A New Robust ARCH Test and YJ-GARCH Model

众所周知,Engle(1982)的ARCH检验对于条件均值模型误设并不稳健,特别地,当条件均值是非线性过程而我们仅对之建立线性模型时,它过度地拒绝真实的原假设,导致出现严重的水平扭曲。因此,本文在文献当中首次利用Yeo-Johnson变换方法来转换均值模型的因变量以排除ARCH过程中均值部分的非线性,进而提出一个新的稳健ARCH检验以及一个新的GARCH模型——Yeo-Johnson(YJ)GARCH模型。蒙特卡罗模拟结果表明,稳健的ARCH检验在水平和势方面的表现要显著优于Engle(1982)的ARCH检验。对上证综指收益率的实证研究结果表明,YJ-GARCH模型的拟合效果要显著优于线性GARCH模型。

It is quite well known that Engle （1982） ＇ s ARCH test is not robust to misspecification of the conditional mean model. Especially, when the conditional mean is nonlinear process and we model it by a linear model, it rejects the true null hypothesis too often and thus causes the serious size distortion. This paper proposes a new robust ARCH test using the Yeo-Johnson transformation in which the dependent variable is transformed to deal with nonlinearity. This alternative model specification yields a new GARCH model, i.e. Yeo-Johnson （YJ） GARCH by product. The Monte Carlo simulation results show that the robust ARCH test is significantly superior to Engle （1982） ＇ s ARCH test in terms of the size and power. Empirical application to the returns of Shanghai Composite Index illustrates that the goodness-of-fit for YJ-GARCH model is clearly better than the linear GARCH model.