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On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes

Listed author(s):
  • Fasen, Vicky
  • Fuchs, Florian
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    In this paper we consider a continuous-time autoregressive moving average (CARMA) process (Yt)t∈R driven by a symmetric α-stable Lévy process with α∈(0,2] sampled at a high-frequency time-grid {0,Δn,2Δn,…,nΔn}, where the observation grid gets finer and the last observation tends to infinity as n→∞. We investigate the normalized periodogram In,YΔn(ω)=|n−1/α∑k=1nYkΔne−iωk|2. Under suitable conditions on Δn we show the convergence of the finite-dimensional distribution of both Δn2−2/α[In,YΔn(ω1Δn),…,In,YΔn(ωmΔn)] for (ω1,…,ωm)∈(R∖{0})m and of self-normalized versions of it to functions of stable distributions. The limit distributions differ depending on whether ω1,…,ωm are linearly dependent or independent over Z. For the proofs we require methods from the geometry of numbers.

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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 1 ()
    Pages: 229-273

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:229-273
    DOI: 10.1016/
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    1. Marquardt, Tina, 2007. "Multivariate fractionally integrated CARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1705-1725, October.
    2. Brockwell, Peter J. & Lindner, Alexander, 2009. "Existence and uniqueness of stationary Lévy-driven CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2660-2681, August.
    3. Knight, Keith, 1991. "On the empirical measure of the Fourier coefficients with infinite variance data," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 109-117, August.
    4. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    5. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
    6. Peter J. Brockwell & Vincenzo Ferrazzano & Claudia Klüppelberg, 2012. "High‐frequency sampling of a continuous‐time ARMA process," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 152-160, January.
    7. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-823, September.
    8. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    9. Marquardt, Tina & Stelzer, Robert, 2007. "Multivariate CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 96-120, January.
    10. anonymous, 1991. "Fed upgrades functional cost analysis program," Financial Update, Federal Reserve Bank of Atlanta, issue Win, pages 1-2,6.
    11. Klüppelberg, Claudia & Mikosch, Thomas, 1993. "Spectral estimates and stable processes," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 323-344, September.
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