LONG-RUN COVARIANCE MATRICES FOR FRACTIONALLY INTEGRATED PROCESSES

Peter Phillips and Chang Sik Kim

Econometric Theory, 2007, vol. 23, issue 6, 1233-1247

Abstract: An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d ∈ [0,½). The theory is then applied to deliver formulas for the long-run covariance matrices of multivariate time series with long memory.Phillips acknowledges partial support from a Kelly Fellowship and from the NSF under grant SES 04-142254. This may be proved directly using a Fourier integral asymptotic expansion when the spectrum of the short-memory component is analytic.

Date: 2007
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