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This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the remaining parameters aredoi:10.1080/07350015.2014.1001028 fatcat:z3ontkbse5gz7no2o7kzz2tl4q