Top

Published in:

2020 | OriginalPaper | Chapter

Invertibility of Infinitely Divisible Continuous-Time Moving Average Processes

Author : Orimar Sauri

Published in: XIII Symposium on Probability and Stochastic Processes

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper studies the invertibility property of continuous time moving average processes driven by a Lévy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel involved and the characteristic triplet of the background driving Lévy process.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Box-Ball System: Soliton and Tree Decomposition of Excursions

Bang, H.H.: Spectrum of functions in Orlicz spaces. J. Math. Sci. Univ. Tokyo 4(2), 341–349 (1997)MathSciNetMATH

Barndorff-Nielsen, O.E., Benth, F.E., Veraart, A.: Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19(3), 803–845 (2013)MathSciNetCrossRef

Barndorff-Nielsen, O.E., Maejima, M., Sato K.: Infinite divisibility for stochastic processes and time change. J. Theor. Probab. 19(2), 411–446 (2006)MathSciNetCrossRef

Barndorff-Nielsen, O.E., Sauri, O., Szozda, B.: Selfdecomposable fields. J. Theor. Probab. 30(1), 233–267 (2017)MathSciNetCrossRef

Basse-O’Connor, A.: Some properties of a class of continuous time moving average processes. In: Proceedings of the 18th EYSM, pp. 59–64 (2013)

Basse-O’Connor, A., Nielsen, M., Pedersen, J., Rohde, V.: A continuous-time framework for arma processes. ArXiv e-prints (2017)

Basse-O’Connor, A., Rosiński, J.: Characterization of the finite variation property for a class of stationary increment infinitely divisible processes. Stoch. Process. Appl. 123(6), 1871–1890 (2013)MathSciNetCrossRef

Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, New York (1986)MATH

Brockwell, P.J., Lindner, A.: Existence and uniqueness of stationary Lévy-driven CARMA processes. Stoch. Process. Appl. 119(8), 2660–2681 (2009)CrossRef

10.

Cohen, S., Maejima, M.: Selfdecomposability of moving average fractional Lévy processes. Stat. Probab. Lett. 81(11), 1664–1669 (2011)CrossRef

11.

Comte, F., Renault, E.: Noncausality in continuous time models. Econ. Theory 12, 215–256 (1996)MathSciNetCrossRef

12.

Duistermaat, J., Kolk, J.: Distributions: Theory and Applications. Cornerstones. Birkhäuser, Boston (2010)

13.

Ferrazzano, V., Fuchs, F.: Noise recovery for Lévy-driven CARMA processes and high-frequency behaviour of approximating Riemann sums. Electron. J. Stat. 7, 533–561 (2013)MathSciNetCrossRef

14.

Kaminska, A.: On Musielak-Orlicz spaces isometric to L ₂ or L _∞. Collect. Math. 48(4–6), 563–569 (1997)MathSciNetMATH

15.

Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics. Springer, Berlin (1983)

16.

Pedersen, J., Sauri, O.: On Lévy semistationary processes with a gamma kernel. In: XI Symposium on Probability and Stochastic Processes. Progress in Probability, vol. 69, pp. 217–239. Springer, Cham (2015)

17.

Rajput, B.S., Rosiński, J.: Spectral representations of infinitely divisible processes. Probab. Theory Rel. Fields 82(3), 451–487 (1989)MathSciNetCrossRef

18.

Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. M. Dekkerl, New York (1994)

19.

Sato, K.: Additive processes and stochastic integrals. Illinois J. Math. 50(1–4), 825–851 (2006)MathSciNetCrossRef

20.

Thuong, T.V.: Some colletions of functions dense in an Orlicz space. Acta Math. Vietnam. 25(2), 195–208 (2000)MathSciNetMATH

Title: Invertibility of Infinitely Divisible Continuous-Time Moving Average Processes
Author: Orimar Sauri
Publisher: Springer International Publishing
Book: XIII Symposium on Probability and Stochastic Processes
Print ISBN: 978-3-030-57512-0

Electronic ISBN: 978-3-030-57513-7

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-57513-7_6