COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1611

Long Run Covariance Matrices for Fractionally Integrated Processes

Peter C.B. Phillips and Chang Sik Kim

June 2007

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 < d < 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory.

Keywords: Asymptotic expansion, Autocovariance function, Fourier integral, Long memory, Long run variance, Spectral density

JEL Classification: C22