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2019 Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies
Vicky Fasen-Hartmann, Markus Scholz
Electron. J. Statist. 13(2): 5151-5212 (2019). DOI: 10.1214/19-EJS1636

Abstract

In this paper, we investigate quasi-maximum likelihood (QML) estimation for the parameters of a cointegrated solution of a continuous-time linear state space model observed at discrete time points. The class of cointegrated solutions of continuous-time linear state space models is equivalent to the class of cointegrated continuous-time ARMA (MCARMA) processes. As a start, some pseudo-innovations are constructed to be able to define a QML-function. Moreover, the parameter vector is divided appropriately in long-run and short-run parameters using a representation for cointegrated solutions of continuous-time linear state space models as a sum of a Lévy process plus a stationary solution of a linear state space model. Then, we establish the consistency of our estimator in three steps. First, we show the consistency for the QML estimator of the long-run parameters. In the next step, we calculate its consistency rate. Finally, we use these results to prove the consistency for the QML estimator of the short-run parameters. After all, we derive the limiting distributions of the estimators. The long-run parameters are asymptotically mixed normally distributed, whereas the short-run parameters are asymptotically normally distributed. The performance of the QML estimator is demonstrated by a simulation study.

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Vicky Fasen-Hartmann. Markus Scholz. "Quasi-maximum likelihood estimation for cointegrated continuous-time linear state space models observed at low frequencies." Electron. J. Statist. 13 (2) 5151 - 5212, 2019. https://doi.org/10.1214/19-EJS1636

Information

Received: 1 September 2018; Published: 2019
First available in Project Euclid: 13 December 2019

zbMATH: 07147374
MathSciNet: MR4042406
Digital Object Identifier: 10.1214/19-EJS1636

Subjects:
Primary: 62H12, 91G70
Secondary: 60F05, 62M10

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Vol.13 • No. 2 • 2019
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