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 ∈ [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 part...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2007
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| Online Access: | https://ink.library.smu.edu.sg/soe_research/247 https://ink.library.smu.edu.sg/context/soe_research/article/1246/viewcontent/Long_Run_Covariance_Matrices_2007.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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