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LONG-RUN COVARIANCE MATRICES FOR FRACTIONALLY INTEGRATED PROCESSES

Published online by Cambridge University Press:  06 September 2007

Peter C.B. Phillips  and
Chang Sik Kim
Peter C.B. Phillips
Affiliation:
Cowles Foundation for Research in Economics, Yale University, University of York and University of Auckland
Chang Sik Kim
Affiliation:
Sungkyunkwan University
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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.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 23 , Issue 6 , December 2007 , pp. 1233 - 1247
Copyright
© 2007 Cambridge University Press

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References

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