# Long memory properties and covariance structure of the EGARCH model

Donatas Surgailis; Marie-Claude Viano

ESAIM: Probability and Statistics (2010)

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

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topSurgailis, Donatas, and Viano, Marie-Claude. "Long memory properties and covariance structure of the EGARCH model." ESAIM: Probability and Statistics 6 (2010): 311-329. <http://eudml.org/doc/104295>.

@article{Surgailis2010,

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},

month = {3},

pages = {311-329},

publisher = {EDP Sciences},

title = {Long memory properties and covariance structure of the EGARCH model},

url = {http://eudml.org/doc/104295},

volume = {6},

year = {2010},

}

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

DA - 2010/3//

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/104295

ER -

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