This note investigates the self‐weighted least absolute deviation estimation (SLADE) of a heavy‐tailed continuous threshold autoregressive (TAR) model. It is shown that the SLADE is strongly consistent and asymptotically normal. The SLADE is global in the sense that the convergence rate is first obtained before deriving its limiting distribution. Moreover, a test for the continuity of TAR model is considered. A sign‐based portmanteau test is developed for diagnostic checking. An empirical example is given to illustrate the usefulness of our method. Combined with the results (Yang and Ling, 2017), a complete asymptotic theory on the SLADE of a heavy‐tailed TAR model is established. This enriches asymptotic theory of statistical inference in threshold models.

中文翻译：

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重尾连续阈值自回归模型的自加权 Lad-Based 推理

本笔记研究了重尾连续阈值自回归 (TAR) 模型的自加权最小绝对偏差估计 (SLADE)。结果表明，SLADE 是强一致且渐近正态的。SLADE 是全局的，因为收敛速度是在导出其极限分布之前首先获得的。此外，还考虑了对 TAR 模型连续性的测试。开发了一种基于符号的 portmanteau 测试用于诊断检查。给出了一个经验示例来说明我们方法的有用性。结合结果(Yang and Ling, 2017)，建立了关于重尾TAR模型的SLADE的完备渐近理论。这丰富了阈值模型中统计推断的渐近理论。