Long term prediction of non-linear time series using multiresolution wavelet models

Wei, Hua‐Liang; Billings, S.A.

doi:10.1080/00207170600621447

Cited by 25 publications

(5 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Wavelets have been successfully applied to EEG signal processing and analysis, see for example Schiff et al (1994), Kalayci and Ozdamar (1995), Blanco et al (1998), and Adeli et al (2003), as well as have been widely used in many other fields including nonlinear signal processing and system identification, see for example Billings and Coca (1999), Liu et al (2002), Wei (2005a, 2005b), Wei and Billings (2004a, 2004b, 2006a, and Wei, Billings and Balikhin (2004). However, not much work has been done on exploiting the attractive properties of wavelets and applying them in time-varying system identification.…”

Section: Electroencephalography (Eeg) Is An Important Non-invasive Tementioning

confidence: 99%

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Wei

Billings

Liu

2010

IJMIC

View full text Add to dashboard Cite

Abstract:A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The timevarying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method.

show abstract

Section: Electroencephalography (Eeg) Is An Important Non-invasive Tementioning

confidence: 99%

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Wei

Billings

Liu

2010

IJMIC

View full text Add to dashboard Cite

show abstract

“…This is called iterative prediction [50]- [52]. The other way, called direct prediction, provides a once-completed predictor with a long-term prediction step, and the specified multistep prediction can then be obtained directly from the established predictor in a manner similar to computing one-step predictions [50], [51].…”

Section: Application To Nonlinear Dynamic Modelingmentioning

confidence: 99%

“…The main downside of the direct modeling approach is that it requires different models for different steps ahead prediction. It is generally believed that the iterative prediction approach is in most cases more efficient than the direct approach assuming that the dynamics underlying the time series are correctly specified by the model [50].…”

Section: Application To Nonlinear Dynamic Modelingmentioning

confidence: 99%

“…The essence of modeling is prediction, and forecasting future behavior based on past observations has been a long standing topic in system identification and time series modeling [50]- [52]. According to the different regression vectors used, the identification model for dynamical systems can be categorized as the series-parallel model or NARX model and the parallel model or nonlinear output error model [36].…”

Section: Application To Nonlinear Dynamic Modelingmentioning

confidence: 99%

See 1 more Smart Citation

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Sun

Butts

2014

IEEE Trans. Cybern.

View full text Add to dashboard Cite

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

show abstract

“…According to wavelet theory, the multivariate nonlinear function f (x 1 (t), x 2 (t), • • • , x n (t)) can be expressed as [20][21][22][23][24]…”

Section: Fixed-grid Wavelet Network For a Multiple-inputs Multiple-outputs Systemmentioning

confidence: 99%

Online Prediction of Ship Coupled Heave-Pitch Motions in Irregular Waves Based on a Coarse-and-Fine Tuning Fixed-Grid Wavelet Network

Huang

Jiang²,

Zou

2021

JMSE

View full text Add to dashboard Cite

A method based on a coarse- and fine-tuning fixed-grid wavelet networks is presented for online prediction of the coupled heave-pitch motions of a ship in irregular waves. The online modeling method contains two processes, i.e., coarse tuning and fine tuning. The coarse tuning is used to select the important wavelet terms, while the fine tuning is only used to compute the related coefficients of the selected wavelet terms. The Givens transformation algorithm is applied to realize the fine-tuning process. Due to the continuous fine-tuning process, the computational efficiency is improved significantly. Both simulation data and experimental data are used to verify the modeling method. The prediction results illustrate that the method has the ability to online predict the coupled heave-pitch motions of a ship in irregular waves.

show abstract

Long term prediction of non-linear time series using multiresolution wavelet models

Cited by 25 publications

References 48 publications

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Online Prediction of Ship Coupled Heave-Pitch Motions in Irregular Waves Based on a Coarse-and-Fine Tuning Fixed-Grid Wavelet Network

Contact Info

Product

Resources

About