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Tests for a Structural Break for Nonnegative Integer-Valued Time Series

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Research Papers in Statistical Inference for Time Series and Related Models

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Abstract

We investigate tests for a structural break for nonnegative integer-valued time series. This topic has been intensively studied in recent years. We deal with the model whose conditional expectation is endowed with dependence structures. Unknown parameters of the model are estimated by an M-estimator. Then, we study three types of test statistics: the Wald type, score type, and residual type. First, we show the asymptotic null distributions of these three test statistics, which enable us to construct asymptotically size \(\alpha \) tests. Next, we show the consistency of the tests, that is, the power of the tests converges to one as sample size increases. Finally, numerical study illustrates the finite-sample performance of the tests.

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Acknowledgements

The author would like to express my deepest gratitude to Professor Masanobu Taniguchi for all your support. Your kind and warm guidance always encouraged the author very much. The author is so proud of being your last disciple. The author is grateful to the editors and referee for their instructive comments. The author would also like to thank Doctor Yan Liu and Doctor Akitoshi Kimura for their encouragements and comments. This research was supported by Grant-in-Aid for JSPS Research Fellow Grant Number JP201920060 and Grant-in-Aid for Research Activity Start-up JP21K20338.

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Authors and Affiliations

  1. Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Yuichi Goto

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  1. Yuichi Goto
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Correspondence to Yuichi Goto .

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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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Goto, Y. (2023). Tests for a Structural Break for Nonnegative Integer-Valued 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_7

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