Parameter estimation for an exponential autoregressive time series model by the Newton search and multi-innovation theory

ABSTRACT

This paper focuses on the recursive parameter estimation problem of the exponential autoregressive (ExpAR) model. Applying the Newton search and multi-innovation theory, a multi-innovation Newton recursive algorithm is presented for identifying the ExpAR model. In order to improve the computational efficiency, the hierarchical identification principle is employed to decompose an ExpAR model into two sub-models, and to derive a hierarchical multi-innovation Newton recursive algorithm. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms.

Keywords:

• ExpAR model
• parameter estimation
• Newton search
• hierarchical identification
• multi-innovation identification

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61873111], the Opening Project of State Key Laboratory for Intelligent Control and Decision of Complex Systems (Beijing Institute of Technology, Beijing, PR China) and the 111 Project [grant number B12018].

Notes on contributors

Huan Xu

Huan Xu was born in Yancheng (Jiangsu, China) in 1992. She received her B.Sc. degree from Nantong University (Nantong, China) in 2015. She is currently a Ph.D. student in the School of Internet of Things Engineering, Jiangnan University, Wuxi, China. Her research interests include system modelling, system identification and parameter estimation.

Feng Ding

Feng Ding received the B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and the M.Sc. and Ph.D. degrees both from the Tsinghua University in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University since 2004. His current research interests include model identification and adaptive control. He authored five books on System Identification.

Min Gan

Min Gan received the B.S. degree in Computer Science and Engineering from the Hubei University of Technology (Wuhan, China) in 2004, and the Ph.D. degree in Control Science and Engineering from Central South University (Changsha, China) in 2010. He is currently a Professor with the College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China. His current research interests include statistical learning, system identification, and nonlinear time series analysis.

Ahmed Alsaedi

Ahmed Alsaedi obtained his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modelling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He has published several articles in peer-reviewed journals. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research programme at KAU. Under his great leadership, this programme is running quite successfully and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.

Tasawar Hayat

Tasawar Hayat was born in Khanewal, Punjab, Distinguished National Professor and Chairperson of Mathematics Department at Quaid-I-Azam University is renowned worldwide for his seminal, diversified and fundamental contributions in models relevant to physiological systems, control engineering, climate change, renewable energy, low-carbon technologies, environmental issues, non-Newtonian fluids, wave mechanics, homotopic solutions, stability, nanofluids and in several other areas. He has a honour of being fellow of Pakistan Academy of Sciences, Third World Academy of Sciences (TWAS) and Islamic World Academy of Sciences in the mathematical Sciences. His national and international recognition is evident by the membership of international and national Committees, leadership and motivation, numerous scholarships and fellowships. He has received many national and international awards including Tamgha-i-Imtiaz, Sitara-i-Imtiaz, Khwarizmi Int. award, ISESCO Int. award, TWAS prize for young scientists, Alexander-Von-Humboldt fellowship, etc.