Wavelet Cross-correlation in Bivariate Time-Series Analysis

Detalhes bibliográficos
Autor(a) principal: SOUZA,E.M.
Data de Publicação: 2018
Outros Autores: FÉLIX,V.B.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300391
Resumo: ABSTRACT The estimation of the correlation between independent data sets using classical estimators, such as the Pearson coefficient, is well established in the literature. However, such estimators are inadequate for analyzing the correlation among dependent data. There are several types of dependence, the most common being the serial (temporal) and spatial dependence, which are inherent to the data sets from several fields. Using a bivariate time-series analysis, the relation between two series can be assessed. Further, as one time series may be related to an other with a time offset (either to the past or to the future), it is essential to also consider lagged correlations. The cross-correlation function (CCF), which assumes that each series has a normal distribution and is not autocorrelated, is used frequently. However, even when a time series is normally distributed, the autocorrelation is still inherent to one or both time series, compromising the estimates obtained using the CCF and their interpretations. To address this issue, analysis using the wavelet crosscorrelation (WCC) has been proposed. WCC is based on the non-decimated wavelet transform (NDWT), which is translation invariant and decomposes dependent data into multiple scales, each representing the behavior of a different frequency band. To demonstrate the applicability of this method, we analyze simulated and real time series from different stochastic processes. The results demonstrated that analyses based on the CCF can be misleading; however, WCC can be used to correctly identify the correlation on each scale. Furthermore, the confidence interval (CI) for the results of the WCC analysis was estimated to determine the statistical significance.
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spelling Wavelet Cross-correlation in Bivariate Time-Series AnalysisMultiscale AnalysisTime SeriesCross CorrelationNon-Decimated Wavelet Transform.ABSTRACT The estimation of the correlation between independent data sets using classical estimators, such as the Pearson coefficient, is well established in the literature. However, such estimators are inadequate for analyzing the correlation among dependent data. There are several types of dependence, the most common being the serial (temporal) and spatial dependence, which are inherent to the data sets from several fields. Using a bivariate time-series analysis, the relation between two series can be assessed. Further, as one time series may be related to an other with a time offset (either to the past or to the future), it is essential to also consider lagged correlations. The cross-correlation function (CCF), which assumes that each series has a normal distribution and is not autocorrelated, is used frequently. However, even when a time series is normally distributed, the autocorrelation is still inherent to one or both time series, compromising the estimates obtained using the CCF and their interpretations. To address this issue, analysis using the wavelet crosscorrelation (WCC) has been proposed. WCC is based on the non-decimated wavelet transform (NDWT), which is translation invariant and decomposes dependent data into multiple scales, each representing the behavior of a different frequency band. To demonstrate the applicability of this method, we analyze simulated and real time series from different stochastic processes. The results demonstrated that analyses based on the CCF can be misleading; however, WCC can be used to correctly identify the correlation on each scale. Furthermore, the confidence interval (CI) for the results of the WCC analysis was estimated to determine the statistical significance.Sociedade Brasileira de Matemática Aplicada e Computacional2018-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300391TEMA (São Carlos) v.19 n.3 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.03.0391info:eu-repo/semantics/openAccessSOUZA,E.M.FÉLIX,V.B.eng2018-12-13T00:00:00Zoai:scielo:S2179-84512018000300391Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-12-13T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Wavelet Cross-correlation in Bivariate Time-Series Analysis
title Wavelet Cross-correlation in Bivariate Time-Series Analysis
spellingShingle Wavelet Cross-correlation in Bivariate Time-Series Analysis
SOUZA,E.M.
Multiscale Analysis
Time Series
Cross Correlation
Non-Decimated Wavelet Transform.
title_short Wavelet Cross-correlation in Bivariate Time-Series Analysis
title_full Wavelet Cross-correlation in Bivariate Time-Series Analysis
title_fullStr Wavelet Cross-correlation in Bivariate Time-Series Analysis
title_full_unstemmed Wavelet Cross-correlation in Bivariate Time-Series Analysis
title_sort Wavelet Cross-correlation in Bivariate Time-Series Analysis
author SOUZA,E.M.
author_facet SOUZA,E.M.
FÉLIX,V.B.
author_role author
author2 FÉLIX,V.B.
author2_role author
dc.contributor.author.fl_str_mv SOUZA,E.M.
FÉLIX,V.B.
dc.subject.por.fl_str_mv Multiscale Analysis
Time Series
Cross Correlation
Non-Decimated Wavelet Transform.
topic Multiscale Analysis
Time Series
Cross Correlation
Non-Decimated Wavelet Transform.
description ABSTRACT The estimation of the correlation between independent data sets using classical estimators, such as the Pearson coefficient, is well established in the literature. However, such estimators are inadequate for analyzing the correlation among dependent data. There are several types of dependence, the most common being the serial (temporal) and spatial dependence, which are inherent to the data sets from several fields. Using a bivariate time-series analysis, the relation between two series can be assessed. Further, as one time series may be related to an other with a time offset (either to the past or to the future), it is essential to also consider lagged correlations. The cross-correlation function (CCF), which assumes that each series has a normal distribution and is not autocorrelated, is used frequently. However, even when a time series is normally distributed, the autocorrelation is still inherent to one or both time series, compromising the estimates obtained using the CCF and their interpretations. To address this issue, analysis using the wavelet crosscorrelation (WCC) has been proposed. WCC is based on the non-decimated wavelet transform (NDWT), which is translation invariant and decomposes dependent data into multiple scales, each representing the behavior of a different frequency band. To demonstrate the applicability of this method, we analyze simulated and real time series from different stochastic processes. The results demonstrated that analyses based on the CCF can be misleading; however, WCC can be used to correctly identify the correlation on each scale. Furthermore, the confidence interval (CI) for the results of the WCC analysis was estimated to determine the statistical significance.
publishDate 2018
dc.date.none.fl_str_mv 2018-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000300391
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2018.019.03.0391
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dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.19 n.3 2018
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
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instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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