On the sieve M-estimation for a special bilinear time series model with time-functional variance noises

Enwen Zhu, Ziwei Deng, Xiaohui Liu and Zhao Liang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 7, 2067-2091

Abstract: The bilinear model has been frequently used in fields like control theory and economics to model seismic data. In this article, time-functional variance (TFV) noises are embedded into a specific bilinear model. We propose a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator (GMLE) with a sieve method and then provide various inferential techniques based on this GMLE. It is shown that under the finite fourth moment of errors, the GMLE is consistent and asymptotically normally distributed. A simulation study and analysis of real data are additionally carried out to evaluate GMLE’s finite sample performance.

Date: 2025
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DOI: 10.1080/03610926.2024.2358846

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