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

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.

Keywords:

• Asymptotic distribution
• bilinear model
• tme-functional variance noises
• maximum likelihood estimate
• sieve estimate

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Enwen Zhu’s research is supported by the National Natural Science Foundation of China (Grant No. 52338009), and the National Science Fund for Distinguished Young Scholars (Grant No. 52025085). Zhao Liang’s research is supported by the Graduate Research Innovation Project of Hunan Province (Grant No. CX20220952). Xiaohui Liu’s research is supported by the NSF of China (Grant No. 11971208), the National Social Science Foundation of China (Grant No. 21 & ZD152), the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province (Grant No. 20224ACB211003), and the NSF of China (Grant No. 92358303).