Threshold Estimation via Group Orthogonal Greedy Algorithm

Abstract

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.

KEY WORDS:

• High-dimensional regression
• Information criteria
• Multiple-regime
• Multiple-threshold
• Nonlinear time series

ACKNOWLEDGMENTS

We would like to thank an Associate Editor and two anonymous referees for their thoughtful and useful comments, which led to an improved version of this article. Research supported in part by HKSAR-RGC-GRF Nos: 400313, 14300514 and HKSAR-RGC-CRF: CityU8/CRG/12G (Chan); Academia Sinica Investigator Award (Ing), HKSAR-RGC-ECS: 405012 and HKSAR-RGC-GRF: 405113, 14601015 (Yau). Part of this research was conducted while N. H. Chan was visiting Renmin University of China (RUC) and Southwestern University of Finance and Economics (SWUFE). Research supported by the School of Statistics at RUC and SWUFE is gratefully acknowledged.