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Empirical Likelihood Approaches for Financial Returns

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Statistical Inference for Financial Engineering

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

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Abstract

We deal with an empirical likelihood and apply it to several financial problems. Empirical likelihood is one of the nonparametric methods of statistical inference. It allows us to use likelihood methods although we do not assume that the data comes from a known family. Consequently, the empirical likelihood has both effectiveness and flexibility of the likelihood method, and reliability of the nonparametric methods. The construction of this chapter is as follows. We briefly look at the history of the empirical likelihood in Sect. 2.1 and review its method for i.i.d. data in Sect. 2.2. The frequency domain approach of empirical likelihood for multivariate non-Gaussian linear processes is discussed in Sect. 2.3. Section 2.4 gives extensions of the empirical likelihood such as Cressie-Read power-divergence statistic and generalized empirical likelihood. Section 2.5 considers application of the generalized empirical likelihood to an inference problem for multivariate stable distributions. Technical proofs of the theorems are given in Sect. 2.6.

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Notes

  1. 1.

    This data is a part of the data set which was used in Dominicy and Veredas (2013).

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Authors and Affiliations

  1. Department of Applied Mathematics, Waseda University, Tokyo, Japan

    Masanobu Taniguchi

  2. Faculty of Economics, Wakayama University, Wakayama, Japan

    Tomoyuki Amano

  3. School of Business Administration, Faculty of Urban Liberal Arts, Tokyo Metropolitan University, Tokyo, Japan

    Hiroaki Ogata

  4. School of International Liberal Studies, Waseda University, Tokyo, Japan

    Hiroyuki Taniai

Authors
  1. Masanobu Taniguchi
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  2. Tomoyuki Amano
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  3. Hiroaki Ogata
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  4. Hiroyuki Taniai
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Correspondence to Masanobu Taniguchi .

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Taniguchi, M., Amano, T., Ogata, H., Taniai, H. (2014). Empirical Likelihood Approaches for Financial Returns. In: Statistical Inference for Financial Engineering. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-03497-3_2

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