COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Post Office Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 872

"Spectral Regression for Cointegrated Time Series"

Peter C.B. Phillips

April 1988

This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including efficient and band spectral methods as well as system and single equation techniques. It is shown that single equation spectral regressions suffer asymptotic bias and nuisance parameter problems that render these regressions impotent for inferential purposes. By contrast systems methods are shown to be covered by LAMN asymptotic theory, bringing the advantages of asymptotic media unbiasedness, scale nuisance parameters and the convenience of asymptotic chi-squared tests. System spectral methods also have advantages over full system direct maximum likelihood in that they do not require complete specification of the error processes. Instead they offer a nonparametric treatment of regression errors which avoids certain methodological problems of dynamic specification and permits additional generality in the class of error processes.

JEL Classification: 211

Keywords: ARMA Model, co-integration, error correction, LAMN family, nonparametric, spectral regression

See CFP 796