Simulation and application of subsampling for threshold autoregressive moving-average models

Abstract

This article considers subsampling inference for threshold ARMA (TARMA) models. Of main interest is inference for the threshold parameter, for which it is known that the limiting distribution of the corresponding estimator is non-normal and very complicated. A simple approach based on a subsampling method is proposed to construct asymptotically valid confidence intervals for the threshold parameter. It is demonstrated that our method furnishes a valid inference for the threshold parameter. The performance of this method in finite samples is evaluated through simulation studies.

Keywords:

• Confidence intervals
• Least squares estimation
• Subsampling
• TARMA model

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62F25
• 62G09
• 62M10

Additional information

Funding

Dong Li acknowledges partially the support of the National Natural Science Foundation of China (NSFC) (No. 11571348 and No. 11771239). Muyi Li acknowledges the support of the NSFC) (No. 71671150), MOE Key Laboratory of Economics (Xiamen University) and Fujian Key Laboratory of Statistical Science.