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A Minimum Contrast Estimation for Spectral Densities of Multivariate Time Series

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Research Papers in Statistical Inference for Time Series and Related Models

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Abstract

We propose a minimum contrast estimator for multivariate time series in the frequency domain. This extension has not been thoroughly investigated, although the minimum contrast estimator for univariate time series has been studied for a long time. The proposal in this paper is based on the prediction errors of parametric time series models. The properties of the proposed contrast estimation function are explained in detail. We also derive the asymptotic normality of the proposed estimator and compare the asymptotic variance with the existing results. The asymptotic efficiency of the proposed minimum contrast estimation is also considered. The theoretical results are illustrated by some numerical simulations.

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Notes

  1. 1.

    The extension to the vector parameter \(\boldsymbol{\theta }\in \Theta \subset \mathbb {R}^d\), \(d > 2\), is straightforward, but the formula for \(V(\boldsymbol{\theta })\) in Theorem 12.1 will be lengthy but not sufficiently fruitful for this paper. This leads to the thought of only presenting the case \(\theta \in \mathbb {R}\).

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Acknowledgements

The author was supported by JSPS Grant-in-Aid for Scientific Research (C) 20K11719. He also would like to express his thanks to the Institute for Mathematical Science (IMS), Waseda University, for their kind hospitality.

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Authors and Affiliations

  1. Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Yan Liu

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  1. Yan Liu
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Correspondence to Yan Liu .

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Editors and Affiliations

  1. Faculty of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo, Japan

    Yan Liu

  2. Faculty of Science, Niigata University, Nishi-ku, Niigata, Japan

    Junichi Hirukawa

  3. Faculty of Economics and Business, Hokkaido University, Kita-ku, Sapporo, Hokkaido, Japan

    Yoshihide Kakizawa

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Liu, Y. (2023). A Minimum Contrast Estimation for Spectral Densities of Multivariate Time Series. In: Liu, Y., Hirukawa, J., Kakizawa, Y. (eds) Research Papers in Statistical Inference for Time Series and Related Models. Springer, Singapore. https://doi.org/10.1007/978-981-99-0803-5_12

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