Rank-based Inference for Multivariate Nonlinear and Long-memory Time Series Models

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  • Hirukawa Junichi
    Department of Mathematics, Faculty of Science, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan.
  • Taniai Hiroyuki
    School of International Liberal Studies, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan.
  • Hallin Marc
    Institut de Recherche en Statistique, ECARES, Université libre de Bruxelles, CP 114, B-1050, Bruxelles, Belgium, ORFE, Princeton University, CentER, University of Tilburg, and ECORE.
  • Taniguchi Masanobu
    Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.

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The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. % through the maximum invariant property of ranks. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.

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