论文标题
线性双重回归模型的准最大最大可能性推断
Quasi-maximum Likelihood Inference for Linear Double Autoregressive Models
论文作者
论文摘要
本文研究了准最大的可能性推断，包括线性双自回旋（DAR）模型的估计，模型选择和诊断检查，其中仅在观察到的过程的分数下建立了所有渐近特性。我们为线性DAR模型提出了高斯准最大可能性估计量（G-QMLE）和一个指数级准最大似然估计器（E-QMLE），并为两个估计量建立了一致性和渐近正态性。基于G-QMLE和E-QMLE，提出了两个贝叶斯信息标准以进行模型选择，并构建了两个混合的Portmanteau测试以检查拟合模型的充分性。此外，我们将所提出的G-QMLE和E-QMLE与现有的双重加权分位数回归估计量相比，就渐近效率和数值性能而言。仿真研究说明了所提出的推理工具的有限样本性能，而比特币返回系列的一个真实示例显示了所提出的推理工具的有用性。
This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only fractional moment of the observed process. We propose a Gaussian quasi-maximum likelihood estimator (G-QMLE) and an exponential quasi-maximum likelihood estimator (E-QMLE) for the linear DAR model, and establish the consistency and asymptotic normality for both estimators. Based on the G-QMLE and E-QMLE, two Bayesian information criteria are proposed for model selection, and two mixed portmanteau tests are constructed to check the adequacy of fitted models. Moreover, we compare the proposed G-QMLE and E-QMLE with the existing doubly weighted quantile regression estimator in terms of the asymptotic efficiency and numerical performance. Simulation studies illustrate the finite-sample performance of the proposed inference tools, and a real example on the Bitcoin return series shows the usefulness of the proposed inference tools.
