Long memory properties and covariance structure of the EGARCH model

Donatas Surgailis; Marie-Claude Viano

ESAIM: Probability and Statistics (2002)

  • Volume: 6, page 311-329
  • ISSN: 1292-8100

Abstract

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The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a hyperbolic decay of the later covariance implies a similar hyperbolic decay of the former covariances. We show, in this case, that normalized partial sums of powers of the observed process tend to fractional brownian motion. The paper also obtains a (functional) CLT for the corresponding partial sums’ processes of the EGARCH model with short and moderate memory. These results are applied to study asymptotic behavior of tests for long memory using the R/S statistic.

How to cite

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Surgailis, Donatas, and Viano, Marie-Claude. "Long memory properties and covariance structure of the EGARCH model." ESAIM: Probability and Statistics 6 (2002): 311-329. <http://eudml.org/doc/245716>.

@article{Surgailis2002,
abstract = {The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a hyperbolic decay of the later covariance implies a similar hyperbolic decay of the former covariances. We show, in this case, that normalized partial sums of powers of the observed process tend to fractional brownian motion. The paper also obtains a (functional) CLT for the corresponding partial sums’ processes of the EGARCH model with short and moderate memory. These results are applied to study asymptotic behavior of tests for long memory using the R/S statistic.},
author = {Surgailis, Donatas, Viano, Marie-Claude},
journal = {ESAIM: Probability and Statistics},
keywords = {EGARCH models; long-memory; partial sums; rescaled range},
language = {eng},
pages = {311-329},
publisher = {EDP-Sciences},
title = {Long memory properties and covariance structure of the EGARCH model},
url = {http://eudml.org/doc/245716},
volume = {6},
year = {2002},
}

TY - JOUR
AU - Surgailis, Donatas
AU - Viano, Marie-Claude
TI - Long memory properties and covariance structure of the EGARCH model
JO - ESAIM: Probability and Statistics
PY - 2002
PB - EDP-Sciences
VL - 6
SP - 311
EP - 329
AB - The EGARCH model of Nelson [29] is one of the most successful ARCH models which may exhibit characteristic asymmetries of financial time series, as well as long memory. The paper studies the covariance structure and dependence properties of the EGARCH and some related stochastic volatility models. We show that the large time behavior of the covariance of powers of the (observed) ARCH process is determined by the behavior of the covariance of the (linear) log-volatility process; in particular, a hyperbolic decay of the later covariance implies a similar hyperbolic decay of the former covariances. We show, in this case, that normalized partial sums of powers of the observed process tend to fractional brownian motion. The paper also obtains a (functional) CLT for the corresponding partial sums’ processes of the EGARCH model with short and moderate memory. These results are applied to study asymptotic behavior of tests for long memory using the R/S statistic.
LA - eng
KW - EGARCH models; long-memory; partial sums; rescaled range
UR - http://eudml.org/doc/245716
ER -

References

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