Statistical estimation of optimal portfolios for locally stationary returns of assets

Hiroshi Shiraishi*, Masanobu Taniguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2007 Feb


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

ASJC Scopus subject areas

  • General Economics,Econometrics and Finance
  • Finance


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