Bootstrapping Spurious Regression
The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap eﬀectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coeﬀicient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even ﬁrst order consistent. The block bootstrap serial correlation coeﬀicient does converge to unity and is therefore ﬁrst order consistent, but has a slower rate of convergence and a diﬀerent limit distribution from that of the sample data serial correlation coeﬀicient. The analysis covers spurious regressions involving both deterministic trends and stochastic trends. The results reinforce earlier warnings about routine use of the bootstrap with dependent data.
Phillips, Peter C.B., "Bootstrapping Spurious Regression" (2001). Cowles Foundation Discussion Papers. 1592.