Abstract
In this paper, we extend the residual-based Dickey–Fuller (DF) and Zt cointegration tests to allow for time-varying variance and obtain their asymptotic null distributions under this circumstance. To deal with time-varying variance, we develop two corresponding tests by wild bootstrap algorithm. The bootstrap-based tests achieve asymptotic validity in the presence of time-varying volatility. Simulations show that the bootstrap tests perform well in finite samples. Applying our proposed method to the Bitcoin and the Chinese stock market, we find evidence that the Bitcoin market is isolated from the Chinese stock market.
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