On the Least Squares Estimation of Multiple-Threshold-Variable Autoregressive Models
研究了包含两个及以上阈值变量的自回归模型的最小二乘估计，证明了阈值估计量的渐近独立性，并提出了加权Nadaraya-Watson方法构建置信区间，适用于阈值变量内生或外生情形。
Most threshold models to-date contain a single threshold variable. However, in many empirical applications, models with multiple threshold variables may be needed and are the focus of this article. For the sake of readability, we start with the Two-Threshold-Variable Autoregressive (2-TAR) model and study its Least Squares Estimation (LSE). Among others, we show that the respective estimated thresholds are asymptotically independent. We propose a new method, namely the weighted Nadaraya-Watson method, to construct confidence intervals for the threshold parameters, that turns out to be, as far as we know, the only method to-date that enjoys good probability coverage, regardless of whether the threshold variables are endogenous or exogenous. Finally, we describe in some detail how our results can be extended to the K-Threshold-Variable Autoregressive (K-TAR) model, K > 2. We assess the finite-sample performance of the LSE by simulation and present two real examples to illustrate the efficacy of our modeling.