Kernel autoregressive models using Yule-Walker equations

Autor: Maya Kallas, Paul Honeine, Hassan Amoud, Clovis Francis
Přispěvatelé: Laboratoire Modélisation et Sûreté des Systèmes (LM2S), Institut Charles Delaunay (ICD), Université de Technologie de Troyes (UTT)-Centre National de la Recherche Scientifique (CNRS)-Université de Technologie de Troyes (UTT)-Centre National de la Recherche Scientifique (CNRS), Faculty of Engineering I, Lebanese University [Beirut] (LU)
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Mathematical optimization
Yule–Walker equations
Computational complexity theory
02 engineering and technology
pre-image problem
time series prediction
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG]
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing
adaptive filtering
0202 electrical engineering
electronic engineering
information engineering
Applied mathematics
Autoregressive integrated moving average
Electrical and Electronic Engineering
Time series
Mathematics
Nonlinear autoregressive exogenous model
autoregressive model
020206 networking & telecommunications
kernel machines
Nonlinear system
machine learning
Autoregressive model
Control and Systems Engineering
Kernel (statistics)
Signal Processing
020201 artificial intelligence & image processing
Computer Vision and Pattern Recognition
[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Software
STAR model
Zdroj: Signal Processing
Signal Processing, 2013, 93 (11), pp.3053-3061. ⟨10.1016/j.sigpro.2013.03.032⟩
Signal Processing, Elsevier, 2013, 93 (11), pp.3053-3061. ⟨10.1016/j.sigpro.2013.03.032⟩
ISSN: 0165-1684
1872-7557
DOI: 10.1016/j.sigpro.2013.03.032⟩
Popis: International audience; This paper proposes nonlinear autoregressive (AR) models for time series, within the framework of kernel machines. Two models are investigated. In the first proposed model, the AR model is defined on the mapped samples in the feature space. In order to predict a future sample, this formulation requires to solve a pre-image problem to get back to the input space. We derive an iterative technique to provide a fine-tuned solution to this problem. The second model bypasses the pre-image problem, by defining the AR model with an hybrid model, as a tradeoff considering the computational time and the precision, by comparing it to the iterative, fine-tuned, model. By considering the stationarity assumption, we derive the corresponding Yule–Walker equations for each model, and show the ease of solving these problems. The relevance of the proposed models is studied on several time series, and compared with other well-known models in terms of accuracy and computational complexity.
Databáze: OpenAIRE
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