COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1330 Bootstrapping Spurious Regression Peter C. B. Phillips September 2001 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. Key words: Asymptotic theory, Bootstrap, Brownian motion, Cointegration, LK representation, Nonstationarity, Residual diagnostics, Unit root JEL Classification: C22 AMS 1991 subject classification: 62M10 |
