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

H. Doosti; M. S. Islam; Y. P. Chaubey; P. Góra

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 journal › Article › peer-review

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 language	English
Pages (from-to)	39-62
Number of pages	24
Journal	Italian Journal of Pure and Applied Mathematics
Issue number	27
Publication status	Published - Dec 2010
Externally published	Yes

Keywords

Besov space
multiresolution analysis
random design
two-dimensional wavelet
wavelets

Cite this

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title = "Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system",

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.",

keywords = "Besov space, multiresolution analysis, random design, two-dimensional wavelet, wavelets",

author = "H. Doosti and Islam, {M. S.} and Chaubey, {Y. P.} and P. G{\'o}ra",

year = "2010",

month = dec,

language = "English",

pages = "39--62",

journal = "Italian Journal of Pure and Applied Mathematics",

issn = "1126-8042",

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T1 - Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system

AU - Doosti, H.

AU - Islam, M. S.

AU - Chaubey, Y. P.

AU - Góra, P.

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

KW - Besov space

KW - multiresolution analysis

KW - random design

KW - two-dimensional wavelet

KW - wavelets

UR - http://www.scopus.com/inward/record.url?scp=79960205577&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79960205577

SP - 39

EP - 62

JO - Italian Journal of Pure and Applied Mathematics

JF - Italian Journal of Pure and Applied Mathematics

SN - 1126-8042

IS - 27

ER -

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

Abstract

Keywords

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