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Some asymptotic results in dependence modelling
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis consists of two papers, both devoted to the study of asymptotics in dependence modelling.

The first paper studies large deviation probabilities for a sum of dependent random variables, where the dependence stems from a few underlying random variables, so-called factors. Each summand is composed of two parts: an idiosyncratic part and a part given by the factors. Conditions under which both factors and idiosyncratic components contribute to the large deviation behaviour are found and the resulting approximation is evaluated in a simple special case. The results are then applied to stochastic processes with the same structure. Based on the results of the first part of the paper, it is concluded that large deviations on a finite time interval are due to one large jump that can come from either the factor or the idiosyncratic part of the process.

The second paper studies the asymptotic eigenvalue distribution of the exponentially weighted moving average (EWMA) covariance estimator. Equations for the limiting eigenvalue density and the boundaries of its support are found using the Marchenko-Pastur theorem.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , iii p.
Series
Trita-MAT, ISSN 1401-2286 ; 2007:01
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-4519ISBN: 978-91-7178-792-7 (print)OAI: oai:DiVA.org:kth-4519DiVA: diva2:12650
Presentation
2007-11-05, 3733, Matematiska Institutionen, Lindstedtsvägen 25, Stockholm, 15:30
Opponent
Supervisors
Note
QC 20101119Available from: 2007-11-07 Created: 2007-11-07 Last updated: 2010-11-19Bibliographically approved
List of papers
1. The asymptotic spectrum of the EWMA covariance estimator
Open this publication in new window or tab >>The asymptotic spectrum of the EWMA covariance estimator
2007 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, no 385, 621-630 p.Article in journal (Refereed) Published
Abstract [en]

The exponentially weighted moving average (EWMA) covariance estimator is a standard estimator for financial time series, and its spectrum can be used for so-called random matrix filtering. Random matrix filtering using the spectrum of the sample covariance matrix is an established tool in finance and signal detection and the EWMA spectrum can be used analogously. In this paper, the asymptotic spectrum of the EWMA covariance estimator is calculated using the Mar enko-Pastur theorem. Equations for the spectrum and the boundaries of the support of the spectrum are obtained and solved numerically. The spectrum is compared with covariance estimates using simulated i.i.d. data and log-returns from a subset of stocks from the S&P 500. The behaviour of the EWMA estimator in this limited empirical study is similar to the results in previous studies of sample covariance matrices. Correlations in the data are found to only affect a small part of the EWMA spectrum, suggesting that a large part may be filtered out

Keyword
EWMA; random matrix theory; covariance estimation; noise
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-7578 (URN)10.1016/j.physa.2007.07.030 (DOI)000250491900021 ()2-s2.0-34548759639 (Scopus ID)
Note
QC 20100811Available from: 2007-11-07 Created: 2007-11-07 Last updated: 2010-11-19Bibliographically approved
2. Large deviations for heavy-tailed factor models
Open this publication in new window or tab >>Large deviations for heavy-tailed factor models
2009 (English)In: Statistics and Probability Letters, ISSN 0167-7152, Vol. 79, no 3, 304-311 p.Article in journal (Refereed) Published
Abstract [en]

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. Depending on the regions considered, probabilities are determined by different parts of the model.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-7579 (URN)10.1016/j.spl.2008.08.011 (DOI)000263424000005 ()2-s2.0-58149502560 (Scopus ID)
Note
QC 20100811Available from: 2007-11-07 Created: 2007-11-07 Last updated: 2010-11-19Bibliographically approved

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