Penalized quasi-likelihood estimation and model selection with parameters on the boundary of the parameter space
研究了带非负约束的计量时间序列模型中，惩罚似然估计和模型选择如何得到标准渐近正态分布，并应用于ARCH模型，模拟和实证显示效果良好。
Summary We consider here penalized likelihood-based estimation and model selection applied to econometric time series models, which allow for nonnegativity (boundary) constraints on some or all of the parameters. We establish that joint model selection and estimation result in standard asymptotic Gaussian distributed estimators. The results contrast with nonpenalized estimation, which, as is well-known, leads to nonstandard asymptotic distributions that depend on the unknown number of parameters on the boundary of the parameter space. We apply our results to the rich class of autoregressive conditional heteroskedastic (ARCH) models for time-varying volatility. For the ARCH models, simulations show that penalized estimation and model selection works surprisingly well, even for models with a large number of parameters. An empirical illustration for stock-market return data shows the ability of penalized estimation to select ARCH models that fit nicely the empirical autocorrelation function, and confirms the stylized fact of long-memory in such financial time series data.