Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 1
Trimmed Least Square Estimators for Stable Ar(1) Processes
Authors:
Alina Bazarova University of Cologne, Institute of Biological Physics

Search for other papers by Alina Bazarova in
Current site
Google Scholar
PubMed Close
,
István Berkes Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Search for other papers by István Berkes in
Current site
Google Scholar
PubMed Close
, and
Lajos Horváth University of Utah, Department of Mathematics

Search for other papers by Lajos Horváth in
Current site
Google Scholar
PubMed Close
Pages:
16–23
Online Publication Date:
18 Feb 2022
Publication Date:
26 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2022.00003
Keywords:
autoregressive processes; least square estimator; consistency; trimming; stable errors
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), 3441–3462.

  • [2]

    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), 547–565.

    • Search Google Scholar
    • Export Citation
  • [3]

    Berkes, I., Horváth, L., and Schauer, J. Asymptotics of trimmed CUSUM statistics. Bernoulli 17 (2011), 1344–1367.

  • [4]

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

  • [5]

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

  • [6]

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

    • Search Google Scholar
    • Export Citation
  • [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), 1–16.

    • Search Google Scholar
    • Export Citation
  • [8]

    Davydov, Y. Weak convergence of discontinuous processes to continuous ones. In: Probability theory and mathematical statistics. Amsterdam: Gordon and Breach 1996, pages 15–18.

    • Search Google Scholar
    • Export Citation
  • [9]

    Withers, C. S. Conditions for linear processes to be strong mixing. Z. Wahrsch. verw. Gebiete 57 (1981), 477–480.

  • Collapse
  • Expand
Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

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
  • DOAJ

Publication Model Gold Open Access
Online only
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

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)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2024 0 14 1
Jan 2025 0 31 5
Feb 2025 0 48 3
Mar 2025 0 48 6
Apr 2025 0 14 1
May 2025 0 1 0
Jun 2025 0 0 0