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Estimation of stable CARMA models with an application to electricity spot prices
, 2010
"... We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantage ..."
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Cited by 10 (0 self)
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We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity market. Here we t a CARMA(2,1) model to spot prices from the Singapore New Electricity Market. The quality of the estimates is assessed in a simulation study. The continuous-time modelling aims at a new pricing methodology for energy derivatives.
Multivariate continuous time stochastic volatility models driven by a Lévy process
- Ph.D. thesis, Fakultät für Mathematik, Technische Universität
, 2007
"... Die Dissertation wurde am 12. Juli 2007 bei der Technischen Universität München eingereicht und durch die Fakultät für Mathematik am 28. September 2007 angenom-men. Zusammenfassung Es werden verschiedene multivariate stochastische Modelle in stetiger Zeit eingeführt und aus probabilistischer un ..."
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Cited by 4 (3 self)
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Die Dissertation wurde am 12. Juli 2007 bei der Technischen Universität München eingereicht und durch die Fakultät für Mathematik am 28. September 2007 angenom-men. Zusammenfassung Es werden verschiedene multivariate stochastische Modelle in stetiger Zeit eingeführt und aus probabilistischer und statistischer Sicht im Detail untersucht. Alle diese Modelle werden von Lévyprozessen getrieben und können allgemein für die Model-lierung mehrdimensionaler Beobachtungsreihen verwendet werden. Hierbei liegt in
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"... On the Exponential Process associated with a CARMA-type Process ..."
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Statistical Modelling 2011; 11(5): 447–470 Estimation of stable CARMA models with an application to electricity spot prices
, 2009
"... Abstract: We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary setup: they have a similar structure as the widely used ARMAmodels and provide all a ..."
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Abstract: We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary setup: they have a similar structure as the widely used ARMAmodels and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity market. Here, we fit a CARMA(2,1) model to spot prices from the Singapore New Electricity Market. The quality of the estimates is assessed in a simulation study. The continuous-time modelling aims at a new pricing methodology for energy derivatives. Key words: CARMA model; electricity prices; estimation of CARMA models; stable CARMA model;
Existence and Uniqueness of Stationary Lévy-driven CARMA Processes
"... Necessary and sufficient conditions for the existence of a strictly stationary solu-tion of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given f ..."
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Necessary and sufficient conditions for the existence of a strictly stationary solu-tion of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given for the process as an inte-gral with respect to the background driving Lévy process. The results generalize results obtained earlier for second-order processes and for processes defined by the Ornstein-Uhlenbeck equation.
