Estimating multiple breaks in nonstationary autoregressive models

Chong (1995) and Bai (1997) proposed a sample-splitting method to estimate multiple-break model. However, their studies focused on stationary time series models, in which the identification of first break depends magnitude duration break, testing procedure is needed assist estimation remaining breaks subsamples split by points found earlier. In this paper, we focus nonstationary autoregressive models. Unlike case, show that does not affect whether it will be identified first. Rather, stochastic order signal strength under case constant also square shrinking magnitude. Since usually have different orders models with breaks, one can therefore determine We apply finding Phillips Yu (2011) et al. (2011, 2015a, 2015b). propose an as well asymptotic theory for Some extensions more general are provided, hypothesis test null being unit root model examined. Results numerical simulations empirical study given illustrate finite-sample performance.