Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models
Yaxing Yang; 杨亚星; Shiqing Ling; 凌仕卿
【Abstract】The least squares estimator of the threshold autoregressive (TAR) model may not be consistent when
its tail is less than or equal to 2. Neither theory nor methodology can be applied to model fitting in this
case. This paper is to develop a systematic procedure of statistical inference for the heavy-tailed TAR
model.We first investigate the self-weighted least absolute deviation estimation for th emodel.It is shown
that the estimated slope parameters are √n-consistent and asymptotically normal, and the estimated
thresholds are n-consistent, each of which converges weakly to the smallest minimizer of a compound
Poisson process. Based on this theory, the Wald test statistic is considered for testing the linear restriction
of slope parameters and a procedure is given for inference of threshold parameters. We finally construct
a sign-based portmanteau test for model checking. Simulations are carried out to assess the performance
of our procedure and a real example is given.
该文认为重尾条件下门限自回归模型(TAR)的最小二乘估计不一定是相合的。本文对重尾TAR模型发展了一种系统地统计推断方法。利用模拟实验分析在有限样本下估计方法和检验统计量的表现。最后将本文提出的理论和方法应用到实际例子中。杨亚星，香港科技大学统计学博士，现任厦门大学经济学院统计系与王亚南经济研究院（WISE）助理教授，主要从事金融计量经济学、非线性时间序列分析等领域研究。
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