Electronic Journal of Statistics

Noise recovery for Lévy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums

Vincenzo Ferrazzano and Florian Fuchs

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We consider high-frequency sampled continuous-time autoregressive moving average (CARMA) models driven by finite-variance zero-mean Lévy processes. An $L^{2}$-consistent estimator for the increments of the driving Lévy process without order selection in advance is proposed if the CARMA model is invertible. In the second part we analyse the high-frequency behaviour of approximating Riemann sum processes, which represent a natural way to simulate continuous-time moving average models on a discrete grid. We compare their autocovariance structure with the one of sampled CARMA processes and show that the rule of integration plays a crucial role. Moreover, new insight into the kernel estimation procedure of Brockwell et al. [11] is given.

Article information

Electron. J. Statist., Volume 7 (2013), 533-561.

First available in Project Euclid: 6 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 60G51: Processes with independent increments; Lévy processes
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

CARMA process high-frequency data Lévy process discretely sampled process noise recovery


Ferrazzano, Vincenzo; Fuchs, Florian. Noise recovery for Lévy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums. Electron. J. Statist. 7 (2013), 533--561. doi:10.1214/13-EJS783. https://projecteuclid.org/euclid.ejs/1362579369

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