Yale University & University of Auckland

Bootstrapping Spurious Regression

Email address: peter.phillips@yale.edu

Keywords: Asymptotic theory, Bootstrap, Brownian motion, Cointegration, LK representation, Nonstationarity, Residual diagnostics, Unit root.

JEL Classifications: C22

Abstract:
The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap eectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coecient 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 coecient 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 coecient. 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.

PDF file of paper: phillips.pdf

Session: Bootstrap and Simulation Methods

Time: Sunday, 8 July, 2:15pm - 3:45pm

Room: A