Quasi-likelihood estimation of structure-changed threshold double autoregressive models

This paper investigates the quasi-maximum likelihood estimator (QMLE) of the structure-changed and two-regime threshold double autoregressive model. It is shown that both the estimated threshold and change-point are n-consistent, and they converge weakly to the smallest minimizer of a compound Poisson process and the location of minima of a two-sided random walk, respectively. Other estimated parameters are n−consistent and asymptotically normal. The performance of the QMLE is assessed via simulation studies and a real example is given to illustrate our procedure.