LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory

Pavel Yaskov ()
Additional contact information
Pavel Yaskov: Steklov Mathematical Institute of Russian Academy of Sciences

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 2032-2055

Abstract: Abstract We obtain a weak law of large numbers for quadratic forms of a stationary regular time series, imposing no rate of convergence to zero of its covariance function. We show how this law can be applied in proving universality properties of limiting spectral distributions of sample covariance matrices. In particular, we give another derivation of a recent result of Merlevède and Peligrad, who studied sample covariance matrices generated by IID samples of long memory time series.

Keywords: Quadratic forms; Long memory; Random matrices; Sample covariance matrices; 60B20 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-017-0767-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0767-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-017-0767-z

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().