A bootstrap-based approach for parameter and polyspectral density estimation of a non-minimum phase ARMA process

Abstract

A bootstrap-based methodology is developed for parameter estimation and polyspectral density estimation in the case of the approximating model of the underlying stochastic process being non-minimum phase autoregressive-moving-average (ARMA) type, given a finite realisation of a single time series data. The method is based on a minimum phase/maximum phase decomposition of the system function together with a time reversal step for the parameter and polyspectral confidence interval estimation. Simulation examples are provided to illustrate the proposed method.

Keywords:

• polyspectrum
• bispectrum
• dependent data bootstrap
• probability density estimation
• non-minimum phase system
• time reversal

Additional information

Notes on contributors

Shahnoor Shanta

Shahnoor Shanta received B.Sc. (Honours) and M.Sc. degrees from the Department of Applied Physics, Electronics and Communication Engineering, University of Dhaka, Bangladesh and the M.Sc. degree in Communications and Signal Processing from Imperial College London. She received the Ph.D. degree in Signal Processing from the University of Sheffield, UK in 2009. She is currently working as a post-doctoral fellow in the Department of Electrical and Computer Engineering, University of Ottawa, Canada. Previously she served as a Lecturer in the Department of Applied Physics, Electronics and Communication Engineering, University of Dhaka, Bangladesh. Her research interests include statistical signal processing, speech and signal enhancement, pattern and speech recognition/classification.

Visakan Kadirkamanathan

Visakan Kadirkamanathan received the B.A. and Ph.D. degrees in Electrical and Information Engineering from the University of Cambridge, Cambridge, UK. He is currently the Head of the Department of Automatic Control and Systems Engineering at the University of Sheffield and is also the Director of the Rolls-Royce supported University Technology Centre for Control and Systems Engineering. He is a Professor of Signal and Information Processing and is affiliated to the Centre for Signal Processing and Complex Systems. He has been with the Department since joining Sheffield in 1993. His research interests include nonlinear signal processing, system identification, spatio-temporal modelling, intelligent control and fault diagnosis with applications in systems biology, aerospace systems and the environment. He has co-authored a book on intelligent control and has published more than 150 papers in refereed journals and proceedings of international conferences. Prof Kadirkamanathan is the Co-Editor of the International Journal of Systems Science, the Associate Editor of the International Journal of Automation and Computing and has served as an Associate Editor for the IEEE Transactions on Neural Networks.