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

Abstract

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.

Citation

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

Information

Published: 2013
First available in Project Euclid: 6 March 2013

zbMATH: 1337.62260
MathSciNet: MR3035265
Digital Object Identifier: 10.1214/13-EJS783

Subjects:
Primary: 60G10, 60G51
Secondary: 62M10

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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