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Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence

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This paper shows that large dimensional vector autoregressive (VAR) models of fi nite order can generate long memory in the marginalized univariate series. We derive high-level assumptions under which the fi nal equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two speci fic models. We consider the implications of our findings for the variances of asset returns where the so-called golden-rule of realized variances states that they tend always to exhibit fractional integration of a degree close to 0:4.

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File URL: https://hal-essec.archives-ouvertes.fr/hal-01158524/document
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Paper provided by ESSEC Research Center, ESSEC Business School in its series ESSEC Working Papers with number WP1507.

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Length: 31 pages
Date of creation: Jun 2015
Handle: RePEc:ebg:essewp:dr-15007
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ESSEC Research Center, BP 105, 95021 Cergy, France

Web page: http://www.essec.edu/
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  11. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
  12. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
  13. Altissimo, Filippo & Mojon, Benoit & Zaffaroni, Paolo, 2009. "Can aggregation explain the persistence of inflation?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 231-241, March.
  14. Susanne M. Schennach, 2013. "Long memory via networking," CeMMAP working papers CWP13/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  19. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
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  23. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
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  25. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
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