STATISTICAL ESTIMATION OF OPTIMAL PORTFOLIOS FOR LOCALLY STATIONARY RETURNS OF ASSETS

Hiroshi Shiraishi () and Masanobu Taniguchi ()
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Hiroshi Shiraishi: Waseda University, 1-104 Totsukamachi, Shinjuku-ku, Tokyo, 169-8050, Japan
Masanobu Taniguchi: Waseda University, 1-104 Totsukamachi, Shinjuku-ku, Tokyo, 169-8050, Japan

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 01, 129-154

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: Optimal portfolio; locally stationary process; locally asymptotic normality; asymptotic efficiency; kernel method (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0219024907004093

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