连续型门限模型的统计推断及应用

Statistical inference for threshold models is the academic cutting-edge in nonlinear time series analysis and has wide application background. The continuity of threshold model directly affects the limiting properties of the parameter estimation, which leads to the essential difference in the statistical inference between continuous and discontinuous threshold models. However, the methods and theories on the continuous threshold model are extremely limited at present. This project intends to investigate the statistical inference for continuous TAR model. The main tasks include three parts: (1) Under the heavy-tailed condition, we will consider the weighted least absolute deviation (LAD) estimation for continuous TAR model, and study the asymptotic properties of its parameter estimator. Base on the asymptotic theory, we will further discuss the testing of continuity for threshold model; (2) We extend the continuous TAR model and study the statistical inference of continuous TARMA model; (3) We study the structural properties of continuous TDAR model, and the consistency and asymptotic distribution of the maximum likelihood estimation. Meanwhile, we develop new tools for model diagnostic checking. This project aims to propose some new methods and theories for the parameter estimation and testing of continuous threshold models, and enrich the time series analysis theory. Simulation will be conducted to evaluate the performance of the proposed estimation and testing methods in finite sample, and the application of these methods to the financial research will also be provided.

门限模型的统计推断问题是当前非线性时间序列分析领域的学术前沿，具有广阔的应用背景。门限模型的连续性直接影响参数估计的极限性质，导致连续与不连续两类门限模型的理论推断存在本质区别。目前关于连续门限模型的理论和方法研究极其有限，本项目拟对该类模型的统计推断进行研究。项目任务主要包括以下三点：（1）考虑在重尾条件下连续TAR模型的加权最小绝对离差估计，研究参数估计的相合性及渐近分布，并在此基础上进一步探讨模型的连续性检验问题；（2）将连续TAR模型进行扩展，研究连续TARMA模型的统计推断问题；（3）研究连续门限双自回归模型的结构性质及其极大似然估计的相合性及渐近分布，提出新的模型诊断工具。本项目旨在对连续型门限模型参数估计和模型检验提出新的方法和渐近理论，丰富时间序列分析理论。本研究还将利用模拟实验评价小样本下模型估计与检验的表现，同时将新的方法和理论应用于金融股票研究领域的数据分析。

门限类模型在理论和应用方面有着非常重要的意义。本项目主要对连续型门限模型的理论和方法进行深入研究，主要研究内容包括：(1) 重尾条件下，证明了连续TAR模型的自加权LAD估计的相合性及渐近正态性；(2)基于符号Ljung-Box检验思想构造了portmanteau检验统计量，发展了新的模型诊断工具；(3) 利用子抽样方法分别构造了检验重尾TAR模型和TARMA连续性的统计量，并推导出该检验的理论性质;(4)将连续TAR模型拓展至连续TARMA模型，证明了连续TARMA模型最小二乘估计的渐近性质；(5)将连续TAR模型拓展到连续TDAR模型，研究了模型的结构性质及其拟极大似然估计;(6)将所提出的方法应用到金融股票数据，包括股票成交量、收益等。本项目在理论上，进一步丰富了门限模型的统计推断理论；在应用上，为金融股票市场提供了更精确的量化工具。