Gourieroux Christian, Jasiak Joann
University of Toronto, Toronto, Canada.
Toulouse School of Economics (TSE), Toulouse, France.
J Time Ser Econom. 2023 Mar 7;15(2):151-198. doi: 10.1515/jtse-2022-0016. eCollection 2023 Jul.
The parametric estimators applied by rolling are commonly used for the analysis of time series with nonlinear patterns, including time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of temporally local maximum likelihood (TLML) estimators. We consider the TLML estimators of (a) constant parameters, (b) stochastic, stationary parameters and (c) parameters with the ultra-long run (ULR) dynamics bridging the gap between the constant and stochastic parameters. We show that the weights used in the TLML estimators have a strong impact on the inference. For illustration, we provide a simulation study of the epidemiological susceptible-infected-susceptible (SIS) model, which explores the finite sample performance of TLML estimators of a time varying contagion parameter.
滚动应用的参数估计器通常用于分析具有非线性模式的时间序列，包括时变参数和局部趋势。本文研究了时间局部极大似然（TLML）估计器类中的滚动估计器的性质。我们考虑（a）常数参数、（b）随机平稳参数以及（c）具有超长动态（ULR）的参数（该动态弥合了常数参数和随机参数之间的差距）的TLML估计器。我们表明，TLML估计器中使用的权重对推断有很大影响。为了说明这一点，我们提供了一个流行病学易感-感染-易感（SIS）模型的模拟研究，该研究探讨了时变传染参数的TLML估计器的有限样本性能。
