Statistics and Its Interface
Volume 4 (2011)
On the least squares estimation of threshold autoregressive and moving-average models
Pages: 183 – 196
This paper considers the least squares estimation and establishes its asymptotic theory for threshold autoregressive and moving-average models. Under some mild conditions, it is shown that the estimator of the threshold is $n$-consistent and after normalization it converges weakly to the smallest minimizer of a compound Poisson process, while the estimators of other coefficients are strongly consistent and asymptotically multivariate normal. This paper also provides a numerical method to tabulate the limiting distribution of the estimated threshold in practice. Simulation studies are carried out to assess the performance of the least squares estimation in finite samples.
asymptotic normality, compound Poisson process, consistency, least squares estimation, threshold ARMA model
2010 Mathematics Subject Classification
Primary 62F12, 62M10. Secondary 60G10.