Representations of continuous-time ARMA processes

By Peter J. Brockwell. Journal of Applied Probability, 2004

102 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bfbc934c62ad624840003383d42bc0548d74738

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Peter J. Brockwell
2. Robert Stelzer
3. Ole E. Barndorff-Nielsen
4. Almut E. D. Veraart
5. Fred Espen Benth
6. V. Todorov
7. T. Marquardt
8. Jan Kallsen

In Statistics and Probability

1. Robert Stelzer
2. Ole E. Barndorff-Nielsen
3. Peter J. Brockwell
4. T. Marquardt
5. Almut E. D. Veraart
6. A. Lindner
7. Fred Espen Benth
8. Jan Kallsen

Citations in the corpus

• Multivariate supOU processes (2010, background): “Ornstein–Uhlenbeck-type processes are a special case of the so-called (multivariate) continuous time autoregressive movingaverage (CARMA) processes (see [10, 11, 33]).”
• A Didactic Note on Affine Stochastic Volatility Models (2006, background): “If one considers the other extreme case Z1 = . . . = Zν , one enters the realm of continuous-time ARMA processes proposed by Brockwell (2004).”
• 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”
• Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, background): “It is well known, see, for example, Brockwell, Davis and Yang [36], that a discretely sampled CARMA(p, q) process (for p > q) has a weak ARMA(p, p− 1) representation.”
• Recent results in the theory and applications of CARMA processes (2014, methodology): “Sufficient conditions for the existence of a strictly stationary solution of (28) and (30) were obtained by Brockwell (2001b). Subsequently Brockwell and Lindner (2009), generalizing results of Wolfe (1982) and Sato and Yamazato (1984) for the Lévydriven Ornstein–Uhlenbeck equation, established nece”
• Lévy-driven and fractionally integrated ARMA processes with continuous time parameter (2005, methodology): “In the next section, following Brockwell (2003), we de ne a fractionallyintegrated L evy-driven CARMA process by fractional integration of the correspond-ing CARMA kernel.4.”
• Fractional Lévy processes with an application to long memory moving average processes (2006, methodology): “Typical examples are the stochastic volatility models of Barndorff-Nielsen and Shephard (2001) which are based on Ornstein–Uhlenbeck processes, the CARMA processes (Brockwell 2001), the FICARMA processes (Brockwell 2004) and the stable MA processes (Samorodnitsky and Taqqu 1994).”