Estimating the COGARCH(1,1) model - a first go
نویسندگان
چکیده
We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent. We investigate the quality of our estimators in a simulation study based on the compound Poisson driven COGARCH model. The estimated volatility with corresponding residual analysis is also presented. 2000 MSC Subject Classifications: primary: 91B70, 91B84 secondary: 62F10, 62F12 JEL Classification: C23, C52
منابع مشابه
Multivariate COGARCH(1,1) processes
Multivariate COGARCH(1,1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1,1) process, we analyze its probabilistic propertie...
متن کاملMCMC estimation of the COGARCH(1,1) model
This paper presents a Markov chain Monte Carlo based estimation procedure for the COGARCH(1,1) model driven by a compound Poisson process. The COGARCH model is a continuous-time analogue to the discrete-time GARCH model and captures many of the stylized facts of financial time series, as has been shown in various papers. Principles for the estimation of point processes by MCMC are adapted to th...
متن کاملMethod of moment estimation in the COGARCH(1,1) model
We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are strongly mixing with exponential rate, we show that the resulting estimators are consistent and asymptotically normal. We investigate the empirical quality of our estimators in a simulation study based on...
متن کاملThe COGARCH: A Review, with News on Option Pricing and Statistical Inference
Continuous time models have been elevated to great importance in the modelling of time series data, in response to the successful options pricing model of Black and Scholes (1973), among other things. In 2004, Klüppelberg, Lindner, and Maller introduced the “COGARCH” model as a continuous-time analogue to the enormously influential and successful discrete time GARCH stochastic volatility model ...
متن کاملConditional Maximum Likelihood Estimation of the First-Order Spatial Integer-Valued Autoregressive (SINAR(1,1)) Model
‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...
متن کامل