Volume 6, 2002
New directions in Time Series Analysis (Guest Editor: Philippe Soulier)
|Page(s)||311 - 329|
|Section||New directions in Time Series Analysis (Guest Editor: Philippe Soulier)|
|Published online||15 November 2002|
Long memory properties and covariance structure of the EGARCH model
Vilnius Institute of Mathematics and Informatics,
Akademijos 4, 2600 Vilnius, Lithuania; firstname.lastname@example.org.
2 Université des Sciences et Technologies de Lille, 59655 Villeneuve-d'Ascq Cedex, France; Marie-Claude.Viano@univ-lille1.fr.
The EGARCH model of Nelson  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.
Mathematics Subject Classification: 60F17 / 62M10 / 91B70 / 91B84
Key words: EGARCH models / long-memory / partial sums / rescaled range.
© EDP Sciences, SMAI, 2002
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