Asymptotic properties of mildly explosive processes with locally stationary disturbance

Abstract

In this study, we derive the limiting distribution of the least squares estimator (LSE) and the localized LSE for mildly explosive autoregressive models with locally stationary disturbance and verify that it is Cauchy as in the iid case. We also investigate the limiting distribution of two types of Dickey–Fuller unit root tests, designed for detecting a bubble period in economic time series data, and show that these tests are consistent. To evaluate the methods, we conduct a simulation study and carry out a data analysis using time series data on bitcoin prices.