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2012 Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes
Eckhard Schlemm, Robert Stelzer
Electron. J. Statist. 6(none): 2185-2234 (2012). DOI: 10.1214/12-EJS743

Abstract

We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-time linear state space models and equidistantly observed multivariate Lévy-driven continuous-time 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.

Citation

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Eckhard Schlemm. Robert Stelzer. "Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes." Electron. J. Statist. 6 2185 - 2234, 2012. https://doi.org/10.1214/12-EJS743

Information

Published: 2012
First available in Project Euclid: 30 November 2012

zbMATH: 1295.62020
MathSciNet: MR3020261
Digital Object Identifier: 10.1214/12-EJS743

Subjects:
Primary: 62F10, 62F12, 62M09
Secondary: 60G10, 60G51

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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