Continuous-time GARCH processes

By Peter J. Brockwell, Erdenebaatar Chadraa, A. Lindner. 2006

98 citations recorded by the source corpus.

For an AR(1) process with ARCH(1) errors, we propose empirical likelihood tests for testing whether the sequence is strictly stationary but has infinite variance, or the sequence is an ARCH(1) sequence or the sequence is an iid sequence. Moreover, an empirical likelihood based confidence interval for the parameter in the AR part is proposed. All of these results do not require more than a finite second moment of the innovations. This includes the case of t-innovations for any degree of freedom larger than 2, which serves as a prominent model for real data.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/cea9ed18884230dea549f704a0d2c3723a695dda

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Citations in the corpus

Fluctuations of Lévy Processes with Applications (2014, background): “(3)Gerber and Shiu (1994) dealt with the case of bounded variation spectrally positive Lévy processes; Boyarchenko and Levendorskǐi (2002) handled a class of tempered stable processes; Chan (2004) covers the case of spectrally negative processes; Avram et al.”
Glossary to ARCH (GARCH) (2008, methodology): “Higher order COGARC(p,q) processes have been developed by Brockwell, Chadraa and Lindner (2006) (see also ECOGARCH).”
Lévy–Driven Continuous–Time ARMA Processes (2009, background): “Doob (1944), Phillips (1959), Brockwell (1995)) that the sampled process (Y (nδ))n∈Z with fixed δ > 0 is a (strict) Gaussian ARMA(r, s) process with 0 ≤ s < r ≤ p and spectral density”
Econometric analysis of jump-driven stochastic volatility models (2011, methodology): “This is very similar to the COGARCH modeling (Klüppelberg et al. (2004), Brockwell et al. (2006)) where the jumps in σ2(t) are proportional to the quadratic variation of the discontinuous component of the price.”
Recent results in the theory and applications of CARMA processes (2014, methodology): “Brockwell et al. (2006) give sufficient conditions for the existence of a strictly stationary solution (Vt )t≥0 and its positivity, and show that (Vt )t≥0 has the same autocorrelation structure as a CARMA(p, q − 1) process.”