Continuous-time ARMA processes

By Peter J. Brockwell. 2001

158 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c587d7d96ccb3dc51df4b854b2c3a17fcdf1a632

How researchers see this paper

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

In Economics and Econometrics

In Finance

Citations in the corpus

Dynamic models of long-memory processes driven by Lévy noise (2002, methodology): “ARMA-type processes (with nonfractional derivatives) driven by Lévy noise were earlier investigated in [17], [18].”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, methodology): “This model was analyzed in Brockwell (2001a) and Todorov and Tauchen (2006) among others.”
Multivariate CARMA processes (2007, background): “[3, 4, 5] and references therein) and widely used in various areas of application like engineering, finance and the natural sciences (e.”
Simulation Methods for Lévy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models (2006, methodology): “Motivated by this two-factor structure of volatility, here we propose (following Brockwell 2001b) a Lévy-driven CARMA(2,1) model for the stochastic variance.”
Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, background): “rera [49], and more recently for electricity prices by Garc´ıa, Klu¨ppelberg and Mu¨ller [45], Benth et al. [25]. A CARMA process is the continuous-time analogue of an ARMA time series, see Brockwell [33], Brockwell [34] for deﬁnition and details. More precisely, suppose that for nonnegative integer”
Continuous-time Gaussian autoregression (2007, methodology): “The coefficient b was therefore estimated by a simple one-dimensional maximization of the Gaussian likelihood (GL) of the original discrete observations (as described by Brockwell (2001)), with the estimated coefficients fixed at the values specified above.)”
The Realized Laplace Transform of Volatility (2011, unknown): “Brockwell (2001)) as well as long-memory models where the driving process is a fractional Brownian motion (e.”
Econometric analysis of jump-driven stochastic volatility models (2011, methodology): “Brockwell (2001) extended the Non-Gaussian OU-SV model by considering CARMA memory functions2.”
Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes (2012, background): “s (see, e.g., [8] for a comprehensive introduction); they were ﬁrst deﬁned in [12] in the univariate Gaussian setting and have stimulated a considerable amount of research in recent years (see, e.g., [5] and references therein). In particular, the restriction of the driving process to Brownian motio”
Modeling irregularly spaced residual series as a continuous stochastic process (2005, methodology): “…for example using continuous time W12404 VON ASMUTH AND BIERKENS: IRREGULARLY SPACED RESIDUAL SERIES 9 of 11 W12404 ARMA models in general [e.g., Brockwell, 2001], nonGaussian OUB models [Barndorff-Nielsen and Shephard, 2001] or by superposition of OU type processes [BarndorffNielsen, 1999].”
Activity Signature Functions for High-Frequency Data Analysis (2010, unknown): “…(2003), the COGARCH model of Klüppelberg et al. (2004) for the financial prices as well as the non-Gaussian Ornstein–Uhlenbeck based models of Barndorff-Nielsen and Shephard (2001) and the Lévy-driven continuous-time moving average (CARMA) models of Brockwell (2001) for the stochastic volatility.”
Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference (2007, methodology): “Our approach is similar, but we suggest using a continuous-time autoregressive error model (e.g. Brockwell and Davis, 1996, Brockwell, 2001) because this seems to be a more reasonable representation of continuous-time processes in the catchment and because this significantly facilitates dealing…”
MODELING HIGH-FREQUENCY FINANCIAL DATA BY PURE JUMP PROCESSES (2012, methodology): “…model of Klüppelberg, Lindner and Maller (2004) for the financial prices, as well as the nonGaussian Ornstein–Uhlenbeck-based models of Barndorff-Nielsen and Shephard (2001) and the Lévy-driven continuous-time moving average (CARMA) models of Brockwell (2001) for the stochastic volatility.”
Recent results in the theory and applications of CARMA processes (2014, methodology): “Existence and uniqueness Sufficient conditions for the existence of a strictly stationary solution of (28) and (30) were obtained by Brockwell (2001b).”