Estimating Semiparametric ARCH(oo) Models by Kernel Smoothing Methods1
研究一类半参数ARCH(∞)模型，提出基于核平滑和剖面似然的估计方法，推导参数与非参数成分的分布理论，并通过模拟和标普500指数回报数据验证了非对称新闻冲击函数的存在。
We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the "news impact" function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis. Copyright The Econometric Society 2005.