Advances in Applied Probability

Limit theory for high frequency sampled MCARMA models

Vicky Fasen

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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.

Article information

Adv. in Appl. Probab., Volume 46, Number 3 (2014), 846-877.

First available in Project Euclid: 29 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60F05: Central limit and other weak theorems
Secondary: 91B84: Economic time series analysis [See also 62M10]

Central limit theorem cointegration domain of attraction high-frequency data multivariate CARMA process regular variation Ornstein-Uhlenbeck process sample variance


Fasen, Vicky. Limit theory for high frequency sampled MCARMA models. Adv. in Appl. Probab. 46 (2014), no. 3, 846--877. doi:10.1239/aap/1409319563.

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