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Asymptotic properties of mildly explosive processes with locally stationary disturbance

In this talk the limit distribution of the least squares estimator for mildly explosive autoregressive models with locally stationary disturbance is established, which is shown to be Cauchy as in the iid case. The result is then applied to identify the onset and the end of an explosive period of a financial time series. Simulations and data analysis are conducted to demonstrate the validity of the result.