Long Run Covariance Matrices for Fractionally Integrated Processes
An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d &amp;amp;isin; &amp;amp;lsqb;0,&amp;amp;frac12;). 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.
Cambridge University Press
PHILLIPS, Peter C. B. and CHANG, Sik Kim.
Long Run Covariance Matrices for Fractionally Integrated Processes. (2007). Econometric Theory. 23, (6), 1233-1247. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/247
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