Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes

Authors


Correspondence to: Florian Fuchs, International School of Applied Mathematics, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany

E-mail: ffuchs@ma.tum.de

Abstract

In this article, we consider a continuous-time autoregressive moving average (CARMA) process driven by either a symmetric α-stable Lévy process with α ∈ (0,2) or a symmetric Lévy process with finite second moments. In the asymptotic framework of high-frequency data within a long time interval, we establish a consistent estimate for the normalized power transfer function by applying a smoothing filter to the periodogram of the CARMA process. We use this result to propose an estimator for the parameters of the CARMA process and exemplify the estimation procedure by a simulation study.

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