Abstract

For a stationary ergodic self-exiting threshold autoregressive model with single threshold parameter Chan (1993) obtained the consistency of the least-squares estimator and Qian (1998) proved it for the maximum likelihood estimator. The aim of this paper is to derive the similar results for the M-estimates of the same model under some regularity conditions.

Keywords: Autoregressive threshold model, $M$-estimates, strong consistency.

MSC: 62M10

Pages:  31$-$36     

Volume  54 ,  Issue  1$-$2 ,  2002