A model for long memory conditional heteroscedasticity

Giraitis, Liudas; Robinson, Peter; Сургайлис, Донатас

doi:10.1214/aoap/1019487516

Cited by 84 publications

(125 citation statements)

References 17 publications

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“…A prominent feature of volatility is the presence of long memory, which led, within the GARCH framework, to the development of the integrated GARCH (Engle and Bollerslev (1986)), the fractionally integrated GARCH (Baillie, Bollerslev, and Mikkelsen (1996)) and the linear ARCH (Robinson (1991), Giraitis, Robinson, and Surgailis (2000)) models. With high frequency data, the long persistence in a series of realized volatilities is portrayed by a slow decay in the autocorrelation function (see e.g., Andersen and Bollerslev (1997), Andersen, Bollerslev, Diebold, and Ebens (2001)), and is modeled by means of fractionally integrated ARMA (ARFIMA) processes by Andersen, Bollerslev, Diebold, and Labys (2003), Oomen (2001) and Koopman, Jungbacker, and Hol (2005), among others.…”

Section: Introductionmentioning

confidence: 99%

Modelling and forecasting multivariate realized volatility

2010

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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 University of Konstanz CoFEValeri Voev ‡ University of Aarhus CREATESAbstract This paper proposes a methodology for modelling time series of realized covariance matrices in order to forecast multivariate risks. The approach allows for flexible dynamic dependence patterns and guarantees positive definiteness of the resulting forecasts without imposing parameter restrictions. We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model's forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies that any risk-averse investor, regardless of the type of utility function, would be better-off using our model.JEL classification: C32, C53, G11

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Section: Introductionmentioning

confidence: 99%

Modelling and forecasting multivariate realized volatility

2010

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“…To construct a long-memory nonlinear model, Giraitis et al (2000b) therefore suggest the LARCH(∞) equation , where B (x, y) denotes the beta function…”

Section: Introductionmentioning

confidence: 99%

Rank-based Inference for Multivariate Nonlinear and Long-memory Time Series Models

Hirukawa

Taniai

Hallin

et al. 2010

JJSS

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The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.

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“…in the sense of convergence of finite dimensional distributions, where Z β (τ ) is a β−stable Lévy process with independent increments, see Taqqu The result (51) is typical for "renewal type long memory" and is in deep contrast with the fBM asymptotics of the corresponding partial sums processes in (47) and (33) for the EGARCH and LARCH models. The limit process Z β (τ ) has infinite variance while |r t | δ has finite variance, which means an increase of variability in the distributional limit (51).…”

Section: Regime Switching Sv and Related Modelsmentioning

confidence: 99%

“…The long memory property was rigorously established for some of these models including the Gaussian subordinated stochastic volatility model (Robinson, 2001), with general form of nonlinearity, the FIEGARCH and related exponential volatility models (Harvey, 1998;Surgailis and Viano, 2002), the LARCH model (Giraitis et al, 2000c), the stochastic volatility model of Zaffaroni (1997, 1998). The long memory property (and even the existence of stationary regime) of some other models (FIGARCH, LM-ARCH) has not been theoretically established; see Giraitis et al (2000a) Mikosch andStȃricȃ (2000, 2003), Kazakevičius et al (2004).…”

Section: Introductionmentioning

confidence: 99%