Testing for a unit root with nonstationary nonlinear heteroskedasticity
研究了当波动率由非平稳时间序列的非线性变换驱动时，Dickey-Fuller单位根检验的大样本理论，并提出了有效的自助法检验程序，适用于金融等领域的实际数据。
We provide a large sample theory for the Dickey-Fuller unit root test when the volatility process is driven by a nonlinear transformation of nonstationary time series. Our theory allows the dynamics of future volatilities being affected by the current shock, and involves replacing the nuisance nonlinear function by its consistent kernel estimator. This improves the existing literature for unit root testing with heteroskedasticity by using external data explicitly. We further propose a valid bootstrap procedure to implement the test, which is found to perform well in finite samples. A real data example is also provided