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

摘要

In this article, we consider a continuous-time autoregressive moving average (CARMA) process driven by either a symmetric α-stable Levy process with α∈ (0,2) or a symmetric Levy 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.