Asymptotic Theory on the Least Squares Estimation of Threshold Moving-Average Models

Abstract

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is n-consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the estimators of other coefficients are strongly consistent and asymptotically normal. This paper also provides a resampling method to tabulate the limiting distribution of the estimated threshold in practice, which is the first successful effort in this direction. This resampling method contributes to threshold literature. Simultaneously, simulation studies are carried out to assess the performance of least squares estimation in finite samples. © 2012 Cambridge University Press.