Recent Advances in ARCH Modelling

Giraitis, Liudas; Leipus, Remigijus; Сургайлис, Донатас

doi:10.1007/3-540-34625-2_1

Cited by 33 publications

(37 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proofs of the corresponding statements under condition (14) use the same ideas but are technically more involved.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Long memory properties and covariance structure of the EGARCH model

Сургайлис¹,

Viano

2002

ESAIM: PS

Self Cite

View full text Add to dashboard Cite

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.Mathematics Subject Classification. 60F17, 62M10, 91B70, 91B84.

show abstract

“…The proofs of the corresponding statements under condition (14) use the same ideas but are technically more involved.…”

Section: Resultsmentioning

confidence: 99%

“…Although the leverage effect has been discussed for the EGARCH model (Nelson [29], Bollerslev and Mikkelsen [4]), we have not found a mathematical proof. The leverage effect in the LARCH model is studied in Giraitis et al [14].…”

Section: Remark 24mentioning

confidence: 99%

Long memory properties and covariance structure of the EGARCH model

Сургайлис¹,

Viano

2002

ESAIM: PS

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bollerslev et al (1994), Diebold and Lopez (1995), Palm (1996), and Guégan (1994, Ch. 5), survey developments till the early 1990s; see Giraitis, Leipus and Surgailis (2006) for a very recent survey. Shephard (1996) considers both univariate GARCH and stochastic volatility models.…”

Section: Final Remarks and Further Readingmentioning

confidence: 99%

An Introduction to Univariate GARCH Models

Teräsvirta

2009

Handbook of Financial Time Series

103

View full text Add to dashboard Cite

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may

show abstract

“…An extensive survey of the theory and applications of these regression models is given by [6], [18], and [30]. Other surveys of GARCH(p, q) processes include [23], [21], [3], [19], [32] and [25], [34], and [22]. Introductory surveys include [12] and [11].…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation of Linear Regression Models with GARCH Errors

Hossain¹,

Ghahramani²

2016

JSTA

View full text Add to dashboard Cite

This paper introduces shrinkage estimators for the parameter vector of a linear regression model with conditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace. We derive the asymptotic distributional biases and risks of the shrinkage estimators using a large sample theory. We show that if the shrinkage dimension exceeds two, the relative efficiency of the shrinkage estimator is strictly greater than that of the full model estimator. Furthermore, a Monte Carlo simulation study is conducted to examine the relative performance of the shrinkage estimators with the full model estimator. Our large sample theory and simulation study show that the shrinkage estimators dominate the full model estimator in the entire parameter space. We illustrate the proposed method using a real data set from econometrics.

show abstract

Recent Advances in ARCH Modelling

Cited by 33 publications

References 41 publications

Long memory properties and covariance structure of the EGARCH model

Long memory properties and covariance structure of the EGARCH model

An Introduction to Univariate GARCH Models

Shrinkage Estimation of Linear Regression Models with GARCH Errors

Contact Info

Product

Resources

About