An Empirical Study for the Estimation of Autoregressive Hilbertian Processes by Wavelet Packet Method
Articles
A. Laukaitis
Vilnius Management Academy, Lithuania
Published 2007-01-25
https://doi.org/10.15388/NA.2007.12.1.14722
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Keywords

autoregressive Hilbertian process
functional data analysis
wavelet packet bases
ill-posed inverse problem
residual partial sums processes

How to Cite

Laukaitis A. (2007) “An Empirical Study for the Estimation of Autoregressive Hilbertian Processes by Wavelet Packet Method”, Nonlinear Analysis: Modelling and Control, 12(1), pp. 65-75. doi: 10.15388/NA.2007.12.1.14722.

Abstract

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.

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