Authors:
Alina Bazarova University of Cologne, Institute of Biological Physics

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István Berkes Alfréd Rényi Institute of Mathematics, Budapest, Hungary

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Lajos Horváth University of Utah, Department of Mathematics

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Open access

We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.

  • [1]

    Bazarova, A., Berkes, I., and Horváth, L. Trimmed stable autoregressive processes. Stoch. Proc. Appl. 124 (2014), 34413462.

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    Berkes, I., Horváth, L., Ling, S., and Schauer, J. Testing for structural change of AR model to threshold AR model. J. Time Series Analysis 32 (2011), 547565.

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  • [3]

    Berkes, I., Horváth, L., and Schauer, J. Asymptotics of trimmed CUSUM statistics. Bernoulli 17 (2011), 13441367.

  • [4]

    Billingsley, P. Convergence of probability measures. Wiley, 1968.

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    Bingham, N. H., Goldie, C. M., and Teugels, J. L. Regular variation. Cambridge University Press, 1987.

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    Cline, D. Estimations and Linear Prediction for Regression, Autoregression and ARMA with In_nite Variance Data. PhD Thesis, Colorado State University, Fort Collins, 1983.

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  • [7]

    Csörgő, S., Horváth, L., and Mason, D. M. What portion of the sample makes a partial sum asymptotically stable or normal? Probability Theory and Related Fields 72 (1986), 116.

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  • [8]

    Davydov, Y. Weak convergence of discontinuous processes to continuous ones. In: Probability theory and mathematical statistics. Amsterdam: Gordon and Breach 1996, pages 1518.

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  • [9]

    Withers, C. S. Conditions for linear processes to be strong mixing. Z. Wahrsch. verw. Gebiete 57 (1981), 477480.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)