Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models
研究了重尾和多阈值双自回归模型的推断方法，包括估计阈值和参数、检验阈值数量及模型检验，通过模拟和实例验证了方法的有效性。
This article develops a systematic inference procedure for heavy-tailed and multiple-threshold double autoregressive (MTDAR) models. We first study its quasi-maximum exponential likelihood estimator (QMELE). It is shown that the estimated thresholds are <i>n</i>-consistent, each of which converges weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are n-consistent and asymptotically normal. Based on this theory, a score-based test is developed to identify the number of thresholds in the model. Furthermore, we construct a mixed sign-based portmanteau test for model checking. Simulation study is carried out to access the performance of our procedure and a real example is given.