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Statistical Inference for Self-Exciting Threshold INAR Processes with Missing Values

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Abstract

The time series model with threshold characteristics under fully observations has been explored intensively in recent years. In this article, several methods are proposed to estimate the parameters of the self-exciting threshold integer-valued autoregressive (SETINAR(2,1)) process in the presence of completely random missing data. In order to dispose of the non-equidistance in the observed data, we research the conditional least squares and conditional maximum likelihood inference based on the p-step-ahead conditional distribution of incomplete observations; in addition, three kinds of imputation methods are investigated to deal with the missing values for estimating the parameters of interest. Multiple groups of stochastic simulation studies are carried out to compare the proposed approaches.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Nos. 11871028, 11731015, 11901053).

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Authors and Affiliations

  1. College of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Han Yan

  2. College of Economics, Liaoning University, Shenyang, 110036, People’s Republic of China

    Dehui Wang

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  1. Han Yan
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  2. Dehui Wang
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Correspondence to Dehui Wang.

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Yan, H., Wang, D. Statistical Inference for Self-Exciting Threshold INAR Processes with Missing Values. Commun. Math. Stat. 11, 795–814 (2023). https://doi.org/10.1007/s40304-021-00275-2

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  • DOI: https://doi.org/10.1007/s40304-021-00275-2

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