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Long-Run Covariance Matrices For Fractionally Integrated Processes

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  • Phillips, Peter C.B.
  • Kim, Chang Sik

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.

Suggested Citation

  • Phillips, Peter C.B. & Kim, Chang Sik, 2007. "Long-Run Covariance Matrices For Fractionally Integrated Processes," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1233-1247, December.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:06:p:1233-1247_07
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    Cited by:

    1. Leschinski, Christian, 2017. "On the memory of products of long range dependent time series," Economics Letters, Elsevier, vol. 153(C), pages 72-76.
    2. Robinson Kruse & Christian Leschinski & Michael Will, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," CREATES Research Papers 2016-17, Department of Economics and Business Economics, Aarhus University.
    3. Phillips, Peter C.B., 2009. "Long memory and long run variation," Journal of Econometrics, Elsevier, vol. 151(2), pages 150-158, August.
    4. Qunyong Wang & Na Wu, 2012. "Long-run covariance and its applications in cointegration regression," Stata Journal, StataCorp LP, vol. 12(3), pages 525-542, September.
    5. Christopoulos, Dimitris & McAdam, Peter, 2017. "Do financial reforms help stabilize inequality?," Journal of International Money and Finance, Elsevier, vol. 70(C), pages 45-61.
    6. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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