On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)

Leonid Galtchouk, Victor Konev

    Research output: Contribution to journal › Article

    4 Citations (Scopus)

    Abstract

    For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.

    Original languageEnglish
    Pages (from-to)2616-2636
    Number of pages21
    JournalJournal of Multivariate Analysis
    Volume101
    Issue number10
    DOIs
    Publication statusPublished - Nov 2010

    Fingerprint

    Fisher information matrix
    Stopping Time
    Autoregressive Process
    Asymptotic Normality
    Unstable
    Observed Information
    Fisher Information Matrix
    Least Squares Estimate
    Stability Region
    Unknown Parameters
    Estimate
    Asymptotic distribution
    Asymptotic Behavior
    Trace
    Stopping time
    Autoregressive process
    Asymptotic normality
    Model
    Least squares
    Asymptotic behavior

    Keywords

    • Asymptotic normality
    • Autoregressive process
    • Least squares estimate
    • Sequential estimation

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Numerical Analysis
    • Statistics and Probability

    Cite this

    On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2). / Galtchouk, Leonid; Konev, Victor.

    In: Journal of Multivariate Analysis, Vol. 101, No. 10, 11.2010, p. 2616-2636.

    Research output: Contribution to journal › Article

    Galtchouk, L & Konev, V 2010, 'On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)', Journal of Multivariate Analysis, vol. 101, no. 10, pp. 2616-2636. https://doi.org/10.1016/j.jmva.2010.07.009
    Galtchouk L, Konev V. On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2). Journal of Multivariate Analysis. 2010 Nov;101(10):2616-2636. https://doi.org/10.1016/j.jmva.2010.07.009
    Galtchouk, Leonid ; Konev, Victor. / On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2). In: Journal of Multivariate Analysis. 2010 ; Vol. 101, No. 10. pp. 2616-2636.
    @article{e880ea6da3b2485fa477fd74de2fe868,
    title = "On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)",
    abstract = "For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.",
    keywords = "Asymptotic normality, Autoregressive process, Least squares estimate, Sequential estimation",
    author = "Leonid Galtchouk and Victor Konev",
    year = "2010",
    month = "11",
    doi = "10.1016/j.jmva.2010.07.009",
    language = "English",
    volume = "101",
    pages = "2616--2636",
    journal = "Journal of Multivariate Analysis",
    issn = "0047-259X",
    publisher = "Academic Press Inc.",
    number = "10",

    }

    TY - JOUR

    T1 - On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)

    AU - Galtchouk, Leonid

    AU - Konev, Victor

    PY - 2010/11

    Y1 - 2010/11

    N2 - For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.

    AB - For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.

    KW - Asymptotic normality

    KW - Autoregressive process

    KW - Least squares estimate

    KW - Sequential estimation

    UR - http://www.scopus.com/inward/record.url?scp=77956715400&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77956715400&partnerID=8YFLogxK

    U2 - 10.1016/j.jmva.2010.07.009

    DO - 10.1016/j.jmva.2010.07.009

    M3 - Article

    AN - SCOPUS:77956715400

    VL - 101

    SP - 2616

    EP - 2636

    JO - Journal of Multivariate Analysis

    JF - Journal of Multivariate Analysis

    SN - 0047-259X

    IS - 10

    ER -

    Access to Document