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September 2014 Limit theory for high frequency sampled MCARMA models
Vicky Fasen
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Adv. in Appl. Probab. 46(3): 846-877 (September 2014). DOI: 10.1239/aap/1409319563

Abstract

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn, . . ., nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

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Vicky Fasen. "Limit theory for high frequency sampled MCARMA models." Adv. in Appl. Probab. 46 (3) 846 - 877, September 2014. https://doi.org/10.1239/aap/1409319563

Information

Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 06347587
MathSciNet: MR3254345
Digital Object Identifier: 10.1239/aap/1409319563

Subjects:
Primary: 60F05, 62M10
Secondary: 91B84

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 3 • September 2014
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