Prediction of time series using yule-walker equations with kernels
Résumé
The autoregressive (AR) model is a well-known technique to analyze time series. The Yule-Walker equations provide a straightforward connection between the AR model parameters and the covariance function of the process. In this paper, we propose a nonlinear extension of the AR model using kernel machines. To this end, we explore the Yule-Walker equations in the feature space, and show that the model parameters can be estimated using the concept of expected kernels. Finally, in order to predict once the model identified, we solve a pre-image problem by getting back from the feature space to the input space. We also give new insights into the convexity of the pre-image problem. The relevance of the proposed method is evaluated on several time series.
Mots clés
machine learning
adaptive filtering
autoregressive processes
covariance analysis
prediction theory
time series
time series prediction
Yule-Walker equation
autoregressive model nonlinear extension
covariance function
kernel machine
feature space
model parameter
preimage problem convexity
Mathematical model
Kernel
Time series analysis
Equations
Predictive models
Support vector machines
Signal processing
autoregressive model
Yule-Walker equations
expected kernels
pre-image problem
nonlinear model
| Origine | Fichiers produits par l'(les) auteur(s) |
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