参数在边界上的时间序列模型的惩罚拟似然估计与模型选择
Penalized Quasi-likelihood Estimation and Model Selection in Time Series Models with Parameters on the Boundary
摘要：
我们将Fan和Li（2001）关于惩罚似然估计和模型选择的理论扩展到统计和计量经济模型，这些模型允许对某些或所有参数的非负约束以及时间序列依赖性。它不同于经典的非惩罚似然估计，其中基于似然的估计量和检验统计量的极限分布是非标准的，并且取决于参数空间边界上的未知参数数量。具体来说，我们建立了联合模型选择和估计，结果在标准的渐近高斯分布估计。的结果被施加到丰富的类的自回归条件异方差（ESTA）模型的建模随时间变化的波动。我们从模拟中发现，惩罚的估计和模型选择的作品令人惊讶的是，即使是大量的参数。一个简单的实证说明股票市场收益率数据证实了惩罚估计的能力，以选择适合很好的自相关函数，以及确认金融时间序列数据的长期记忆的程式化的事实的模型。
英文摘要：
We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as time-series dependence. It differs from classic non-penalized likelihood estimation, where limiting distributions of likelihood-based estimators and test-statistics are non-standard, and depend on the unknown number of parameters on the boundary of the parameter space. Specifically, we establish that the joint model selection and estimation, results in standard asymptotic Gaussian distributed estimators. The results are applied to the rich class of autoregressive conditional heteroskedastic (ARCH) models for the modelling of time-varying volatility. We find from simulations that the penalized estimation and model-selection works surprisingly well even for a large number of parameters. A simple empirical illustration for stock-market returns data confirms the ability of the penalized estimation to select ARCH models which fit nicely the autocorrelation function, as well as confirms the stylized fact of long-memory in financial time series data.
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