A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour

By Claudia Klüppelberg, A. Lindner, Ross Maller. Journal of Applied Probability, 2004

286 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/71670c3c9514c545ddbafe04b7c0ca043d53e917

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Citations in the corpus

Fisher's Information for Discretely Sampled Lévy Processes (2004, background): “…(2004)], stochastic volatility modelling [see e.g., Barndorff– Nielsen (1997), Barndorff–Nielsen (1998), Leblanc and Yor (1998), Carr et al. (2003) and Klüppelberg et al. (2004)] or for the purpose of better describing asset returns data [see e.g., Mandelbrot (1963), Fama and Roll (1965),…”
A Didactic Note on Affine Stochastic Volatility Models (2006, background): “An interesting and natural continuous-time extension of GARCH(1,1) has recently been suggested by Kluppelberg et al. (2004) .”
GARCH Models (2010, unknown): “His results were extended by Klüppelberg, Lindner and Maller (2004) to the case of E log+ η2 t = +∞.”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, unknown): “For convenience define Rt := ∑ 0 s≤t (e−∆ξs − 1)∆ηs, t ≥ 0.”
Lévy–Driven Continuous–Time ARMA Processes (2009, methodology): “A continuous-time analog of the GARCH(1,1) process, denoted COGARCH(1,1), has recently been constructed and studied by Klüppelberg et al. (2004). Their construction uses an explicit representation of the discrete-time GARCH(1,1) process to obtain a continuous-time analog.”
Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models (2006, background): “In Klüppelberg, Lindner and Maller [22], the authors proposed a different approach to obtain a continuous time model.”
Continuous-time GARCH processes (2006, background): “The Annals of Applied Probability 2006, Vol. 16, No. 2, 790–826 DOI: 10.1214/105051606000000150 © Institute of Mathematical Statistics, 2006”
Extremal behavior of stochastic volatility models (2006, unknown): “∗Center for Mathematical Sciences, Munich University of Technology, D-85747 Garching, Ger- many, email: {fasen, cklu, lindner}@ma.tum.de, www.ma.tum.de/stat/”
Recent results in the theory and applications of CARMA processes (2014, methodology): “Necessary and sufficient conditions for the existence of a strictly stationary volatility process were obtained by Klüppelberg et al. (2004) and, under certain assumptions, they showed that non-overlapping increments of the corresponding process G are uncorrelated, while the autocorrelation…”
Activity Signature Functions for High-Frequency Data Analysis (2010, methodology): “…variance gamma (Madan et al., 1998), the CGMY model of Carr et al. (2002), the timechanged Lévy models of Carr et al. (2003), the COGARCH model of Klüppelberg et al. (2004) for the financial prices as well as the non-Gaussian Ornstein–Uhlenbeck-based models of BarndorffNielsen and Shephard…”
Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)-Processes (2009, background): “The ARCH(1) case with E log(ε(2)0) = ∞ was added by Klüppelberg et al. (2004). Here, as usual, for a real number x we set log(x) = log(max(1, x)), so that log(ε(2)0) = (log ε(2)0).”
Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals (2005, unknown): “[28].”
Method of Moment Estimation in the Cogarch(1,1) Model (2007, unknown): “4) of [9] we have Cov((G t ) 2, (G t+h) 2) = ( er|Ψ(1)| − 1 |Ψ(1)| ) E(L(2)1)Cov(G 2 r , σ 2 r ) e −h|Ψ(1)| (A.”
Fluctuations of Lévy Processes with Applications (2014, background): “See for example Huzak et al. (2004a,b), Chan (2004) and Klüppelberg et al. (2004).”