Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system

H. Doosti*, M. S. Islam, Y. P. Chaubey, P. Góra

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this note we introduce a new estimator for estimating autoregressive model function based on two-dimensional wavelet expansion of joint density function. We investigate some asymptotic properties of the proposed estimator. We also added the problem of estimating of derivative of autoregressive estimator through new approach. Finally, we apply our method in dynamical systems. In particular, we estimate a chaotic map from a noisy data and filter entropy of the chaotic map.

Original languageEnglish
Pages (from-to)39-62
Number of pages24
JournalItalian Journal of Pure and Applied Mathematics
Issue number27
Publication statusPublished - Dec 2010
Externally publishedYes

Keywords

  • Besov space
  • multiresolution analysis
  • random design
  • two-dimensional wavelet
  • wavelets

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