Threshold Estimation via Group Orthogonal Greedy Algorithm
针对阈值自回归模型中阈值估计的难题，提出将多阈值检测转化为回归变量选择问题，并用分组正交贪婪算法高效估计阈值，理论推导和模拟实验支持了方法的有效性。
A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection problem, and then employs a group orthogonal greedy algorithm to obtain the threshold estimates. Desirable theoretical results are derived to lend support to the proposed methodology. Simulation experiments are conducted to illustrate the empirical performances of the method. Applications to U.S. GNP data are investigated.