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Master's Dissertation
DOI
Document
Author
Full name
Ronaldo Mendes Evaristo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Baccalá, Luiz Antonio (President)
Arjona Ramírez, Miguel
Sato, João Ricardo
Title in Portuguese
Métodos de reamostragem de séries temporais baseados em wavelets.
Keywords in Portuguese
Análise de ondaletas
Análise de séries temporais
Análise espectral
Abstract in Portuguese
Neste texto são revisados métodos de reamostragem de séries temporais discretas baseados em wavelets, como alternativas as abordagens clássicas, feitas nos domínios do tempo e da frequência. Tais métodos, conhecidos na literatura como wavestrap e wavestrapping fazem uso, respectivamente, das transformadas wavelet discreta (DWT) e wavelet packet discreta (DWPT). Existem poucos resultados sobre a aplicação da DWPT, de forma que este texto pode ser considerado uma contribuição. Aqui mostra-se também, a superioridade do wavestrapping sobre o wavestrap quando aplicados na estimação da densidade espectral de potência de séries temporais sintéticas geradas a partir de modelos autoregressivos. Tais séries possuem uma particularidade interessante que são picos, geralmente acentuados, em sua reapresentação espectral, de tal forma que grande parte dos métodos clássicos de reamostragem apresentam resultados viesados quando aplicados a estes casos.
Title in English
Resampling methods for time series based on wavelets.
Keywords in English
Spectral analysis
Time series analysis
Wavelets analysis
Abstract in English
This paper reviews resampling methods based on wavelets as an alternative to the classic approaches which are, made in the time and frequency domains. These methods, known in the literature as wavestrap and wavestrapping, make use, respectively, of the discrete wavelet transform (DWT) and of the discrete wavelet packet transform (DWPT). Since only few results are avaliable when the DWPT is applied, this text can be considered a contribution to the subject. Here we, also show the superiority of wavestrapping over wavestrap when they are applied to the estimation of power spectral densities of the synthetic time series generated from autoregressive models. These series have an interesting feature that are sharp peaks in their spectral representation, so that most of the traditional methods of resampling lead to biased results.
 
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Publishing Date
2010-09-02
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • EVARISTO, R. M., e BACCALÁ, L. A. Reamostragem de Séries Temporais Baseada em Transformada Wavelet Discreta e Transformada Wavelet Discreta por Pacotes. In VIII Encontro Regional de Matemática Aplicada e Computacional, 2008., Natal, RN, 2008. ERMAC - Encontro Regional de Matemática Aplicada e Computacional, 2008., 2008.
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