Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155723 | Stochastic Processes and their Applications | 2013 | 45 Pages |
Abstract
In this paper we consider a continuous-time autoregressive moving average (CARMA) process (Yt)tâR driven by a symmetric α-stable Lévy process with αâ(0,2] sampled at a high-frequency time-grid {0,În,2În,â¦,nÎn}, where the observation grid gets finer and the last observation tends to infinity as nââ. We investigate the normalized periodogram In,YÎn(Ï)=|nâ1/αâk=1nYkÎneâiÏk|2. Under suitable conditions on În we show the convergence of the finite-dimensional distribution of both În2â2/α[In,YÎn(Ï1În),â¦,In,YÎn(ÏmÎn)] for (Ï1,â¦,Ïm)â(Râ{0})m and of self-normalized versions of it to functions of stable distributions. The limit distributions differ depending on whether Ï1,â¦,Ïm are linearly dependent or independent over Z. For the proofs we require methods from the geometry of numbers.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Vicky Fasen, Florian Fuchs,