Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes
arXiv:1210.7447 · doi:10.1214/12-EJS743
Abstract
We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate Lévy-driven continuoustime autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics.
References in corpus (2)
Cited by in corpus (8)
- Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations
- CARMA Processes driven by Non-Gaussian Noise
- Estimation of causal CARMA random fields
- Whittle estimation for stationary state space models with finite second moments
- Statistical inference for continuous-time locally stationary processes using stationary approximations
- Quasi-maximum likelihood estimation for cointegrated continuous-time state space models observed at low frequencies
- Implementation of Lévy CARMA model in Yuima package
- Modeling credit default swap premiums with stochastic recovery rate