Statistical estimation of optimal portfolios for locally stationary returns of assets

Hiroshi Shiraishi, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

    Original languageEnglish
    Pages (from-to)129-154
    Number of pages26
    JournalInternational Journal of Theoretical and Applied Finance
    Volume10
    Issue number1
    DOIs
    Publication statusPublished - 2007 Feb

    Fingerprint

    Optimal portfolio
    Assets
    Estimator
    Statistical estimation
    Local area networks
    Stationary process
    Asymptotic properties
    Asymptotic distribution
    Kernel
    Quasi-maximum likelihood estimator
    Parametric model
    Bandwidth
    Kernel methods

    Keywords

    • Asymptotic efficiency
    • Kernel method
    • Locally asymptotic normality
    • Locally stationary process
    • Optimal portfolio

    ASJC Scopus subject areas

    • Economics, Econometrics and Finance(all)

    Cite this

    Statistical estimation of optimal portfolios for locally stationary returns of assets. / Shiraishi, Hiroshi; Taniguchi, Masanobu.

    In: International Journal of Theoretical and Applied Finance, Vol. 10, No. 1, 02.2007, p. 129-154.

    Research output: Contribution to journalArticle

    @article{cd2e9fff8aed4d44b3cae13f7e8b627c,
    title = "Statistical estimation of optimal portfolios for locally stationary returns of assets",
    abstract = "This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.",
    keywords = "Asymptotic efficiency, Kernel method, Locally asymptotic normality, Locally stationary process, Optimal portfolio",
    author = "Hiroshi Shiraishi and Masanobu Taniguchi",
    year = "2007",
    month = "2",
    doi = "10.1142/S0219024907004093",
    language = "English",
    volume = "10",
    pages = "129--154",
    journal = "International Journal of Theoretical and Applied Finance",
    issn = "0219-0249",
    publisher = "World Scientific Publishing Co. Pte Ltd",
    number = "1",

    }

    TY - JOUR

    T1 - Statistical estimation of optimal portfolios for locally stationary returns of assets

    AU - Shiraishi, Hiroshi

    AU - Taniguchi, Masanobu

    PY - 2007/2

    Y1 - 2007/2

    N2 - This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

    AB - This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

    KW - Asymptotic efficiency

    KW - Kernel method

    KW - Locally asymptotic normality

    KW - Locally stationary process

    KW - Optimal portfolio

    UR - http://www.scopus.com/inward/record.url?scp=33846438586&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33846438586&partnerID=8YFLogxK

    U2 - 10.1142/S0219024907004093

    DO - 10.1142/S0219024907004093

    M3 - Article

    AN - SCOPUS:33846438586

    VL - 10

    SP - 129

    EP - 154

    JO - International Journal of Theoretical and Applied Finance

    JF - International Journal of Theoretical and Applied Finance

    SN - 0219-0249

    IS - 1

    ER -