An Empirical Study for the Estimation of Autoregressive Hilbertian Processes by Wavelet Packet Method - Laukaitis, A. (Nonlinear Analysis: Modelling and Control, 2007)
In this paper wavelet packet bases are used for an estimation of the autoregressive Hilbertian processes operator. We assume that integral operator kernel can have some singular structures and estimate them by projecting functional processes on suitable bases. Linear methods for continuous-time prediction using Hilbert-valued autoregressive processes are compared with the suggested method on simulated data and on real-life data sets. Statistics of residual partial sums processes and Ex poste prediction are used to check the model.