Predicting nonstationary time series with multi-scale Gaussian processes model

Abstract

The Gaussian processes (GP) model has been successfully applied to the prediction of nonstationary time series. Due to the model's covariance function containing an undetermined hyperparameters, to find its maximum likelihood values one usually suffers from either susceptibility to initial conditions or large computational cost. To overcome the pitfalls mentioned above, at the same time to acquire better prediction performance, a novel multi-scale Gaussian processes (MGP) model is proposed in this paper. In the MGP model, the covariance function is constructed by a scaling function with its different dilations and translations, ensuring that the optimal value of the hyperparameter is easy to determine. Although some more time is spent on the calculation of Covariance function, MGP takes much less time to determine hyperparameter. Therefore, the total training time of MGP is competitive to GP. Experiments demonstrate the prediction performance of MGP is better than GP. Moreover, the experiments also show that the performance of MGP and support vector machine (SVM) is comparable. They give better performance compared to the radial basis function (RBF) networks. © Springer-Verlag Berlin Heidelberg 2006.