On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes
The aim of this paper is to investigate a sampled sequence of a casual stable CARMA process if we observe the underlying process at equidistant time points with small distances as are used for modeling high-frequency data and to study the asymptotic behavior of the sampled process in the frequency domain. As the process one considers a continuous-time ARMA process (CARMA) driven by a symmetric \(\alpha\)-stable Lévy process with positive \(\alpha\) not exceeding the upper limit 2. One investigates the normalized periodogram that converges (including its self-normalized versions) under a suitable condition on the sampling pattern to functions of stable distributions. The proofs exploit some methods from the geometry of numbers.
scientific article; zbMATH DE number 6106889