IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3250-d703402.html
   My bibliography  Save this article

Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares

Author

Listed:
  • Dmitriy Ivanov

    (Department of Information Systems Security, Samara National Research University, 443086 Samara, Russia
    Department of Mechatronics, Samara State University of Transport, 443066 Samara, Russia)

  • Aleksandr Zhdanov

    (Department of Applied Mathematics and Computer Science, Samara State Technical University, 443100 Samara, Russia)

Abstract

This paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A total least squares problem is often ill-conditioned. To solve a TLS problem, a classical algorithm based on finding the right singular vector or an algorithm based on an augmented system of equations with complex coefficients can be applied. In this paper, a new augmented system of equations with real coefficients is proposed to solve TLS problems. A symmetrical augmented system of equations was applied to the parameter identification of discrete fractional systems. The simulation results showed that the use of the proposed symmetrical augmented system of equations can shorten the time for solving such problems. It was also shown that the proposed system can have a smaller condition number.

Suggested Citation

  • Dmitriy Ivanov & Aleksandr Zhdanov, 2021. "Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3250-:d:703402
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3250/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3250/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Reisen, Valderio Anselmo & Rodrigues, Alexandre L. & Palma, Wilfredo, 2006. "Estimation of seasonal fractionally integrated processes," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 568-582, January.
    2. Rubén Martínez-González & Yolanda Bolea & Antoni Grau & Herminio Martínez-García, 2009. "An LPV Fractional Model for Canal Control," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-18, July.
    3. Wayne A. Woodward & Q. C. Cheng & H. L. Gray, 1998. "A k‐Factor GARMA Long‐memory Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 485-504, July.
    4. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicholas Apergis & Andrea Mervar & James E. Payne, 2017. "Forecasting disaggregated tourist arrivals in Croatia," Tourism Economics, , vol. 23(1), pages 78-98, February.
    2. Dominique Guegan & Laurent Ferrara, 2008. "Fractional and seasonal filtering," PSE-Ecole d'économie de Paris (Postprint) halshs-00646178, HAL.
    3. Beaumont, Paul & Smallwood, Aaron, 2019. "Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models," MPRA Paper 96314, University Library of Munich, Germany.
    4. Laurent Ferrara & Dominique Guegan & Zhiping Lu, 2008. "Testing fractional order of long memory processes: a Monte Carlo study," Documents de travail du Centre d'Economie de la Sorbonne b08012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    6. Souhir, Ben Amor & Heni, Boubaker & Lotfi, Belkacem, 2019. "Price risk and hedging strategies in Nord Pool electricity market evidence with sector indexes," Energy Economics, Elsevier, vol. 80(C), pages 635-655.
    7. Laurent Ferrara & Dominique Guégan, 2008. "Business surveys modelling with Seasonal-Cyclical Long Memory models," Economics Bulletin, AccessEcon, vol. 3(29), pages 1-10.
    8. Marques, G.O.L.C., 2011. "Empirical aspects of the Whittle-based maximum likelihood method in jointly estimating seasonal and non-seasonal fractional integration parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 8-17.
    9. Silva, E.M. & Franco, G.C. & Reisen, V.A. & Cruz, F.R.B., 2006. "Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1002-1011, November.
    10. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.
    11. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    12. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    13. Rob Hyndman & Heather Booth & Farah Yasmeen, 2013. "Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 261-283, February.
    14. Ngene, Geoffrey & Tah, Kenneth A. & Darrat, Ali F., 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, Elsevier, vol. 34(C), pages 61-73.
    15. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
    16. Alketa Bejko & Etleva Peta & Belinda Xarba, 2015. "The Evaluation of the Drafting Process of Regional’s Development Strategies in Albania. the Research on Gjirokastra’s Region," European Journal of Interdisciplinary Studies Articles, Revistia Research and Publishing, vol. 1, ejis_v1_i.
    17. SangKun Bae & Mark J. Jensen, 1998. "Long-Run Neutrality in a Long-Memory Model," Macroeconomics 9809006, University Library of Munich, Germany, revised 21 Apr 1999.
    18. Jinquan Liu & Tingguo Zheng & Jianli Sui, 2008. "Dual long memory of inflation and test of the relationship between inflation and inflation uncertainty," Psychometrika, Springer;The Psychometric Society, vol. 3(2), pages 240-254, June.
    19. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    20. Erhard Reschenhofer & Manveer K. Mangat, 2021. "Fast computation and practical use of amplitudes at non-Fourier frequencies," Computational Statistics, Springer, vol. 36(3), pages 1755-1773, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3250-:d:703402. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.