A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Statistical inverse estimation in Hilbert scales
SIAM Journal on Applied Mathematics
Wavelet regression for random or irregular design
Computational Statistics & Data Analysis
Classifying functional time series
Signal Processing
Weak convergence in the functional autoregressive model
Journal of Multivariate Analysis
Curve forecasting by functional autoregression
Journal of Multivariate Analysis
Estimation of a change-point in the mean function of functional data
Journal of Multivariate Analysis
Testing the stability of the functional autoregressive process
Journal of Multivariate Analysis
Nonparametric time series forecasting with dynamic updating
Mathematics and Computers in Simulation
Short term local meteorological forecasting using type-2 fuzzy systems
WIRN'05 Proceedings of the 16th Italian conference on Neural Nets
A prediction method for time series based on wavelet neural networks
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part I
Hi-index | 0.00 |
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that represent a generalization of the classical autoregressive processes to random variables with values in a Hilbert space. A careful analysis reveals, in particular, that this approach is related to the theory of function estimation in linear ill-posed inverse problems. In the deterministic literature, such problems are usually solved by suitable regularization techniques. We describe some recent approaches from the deterministic literature that can be adapted to obtain fast and feasible predictions. For large sample sizes, however, these approaches are not computationally efficient.With this in mind, we propose three linear wavelet methods to efficiently address the aforementioned prediction problem. We present regularization techniques for the sample paths of the stochastic process and obtain consistency results of the resulting prediction estimators. We illustrate the performance of the proposed methods in finite sample situations by means of a real-life data example which concerns with the prediction of the entire annual cycle of climatological El Niño-Southern Oscillation time series 1 year ahead. We also compare the resulting predictions with those obtained by other methods available in the literature, in particular with a smoothing spline interpolation method and with a SARIMA model.