Performance bounds for nonlinear time series prediction
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Prequential and Cross-Validated Regression Estimation
Machine Learning
Nonparametric Time Series Prediction Through Adaptive ModelSelection
Machine Learning
Learning from dependent observations
Journal of Multivariate Analysis
IEEE Transactions on Information Theory
Distortion prediction for video quality optimization over packet switched networks
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Automatica (Journal of IFAC)
Brief Finite sample properties of system identification of ARX models under mixing conditions
Automatica (Journal of IFAC)
| Hi-index | 754.90 |
We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process (Xi)i=-∞∞. The best mean-square predictor of X0 is its conditional mean given the entire infinite past (Xi)i=-∞-1. Given a sequence of observations X1, X2, XN, we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension, for example, neural networks and Legendre polynomials. The proposed estimators select both the model memory and the model dimension, in a data-driven fashion, by minimizing certain complexity regularized least squares criteria. When the underlying predictor function has a finite memory, we establish that the proposed estimators are memory-universal: the proposed estimators, which do not know the true memory, deliver the same statistical performance (rates of integrated mean-squared error) as that delivered by estimators that know the true memory. Furthermore, when the underlying predictor function does not have a finite memory, we establish that the estimator based on Legendre polynomials is consistent