Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada
Autor(a) principal: | |
---|---|
Data de Publicação: | 2016 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/7943 |
Resumo: | From the generalized normal distribution and concepts of the generalized autoregressive moving averages models we introduce the generalized normal-ARMA model as an alternative way to model time series exhibiting symmetry and tails that may be lighter or heavier when compared the normal distribution. We present application for proposed model using three time series in the hydrology, economy and publics policy areas. The proposed model is presented as good alternative when compared to ARMA model with normal distribution. We extended this model the case of the asymmetric time series. In this case we used the Box-Cox transformation, denoted by Box-Cox generalized normal ARMA. The particular case, when we use the logarithmic transformation is called generalized log-normal ARMA. We adjusted the models with transformation to the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants. We obtain the prediction values for the model with transformation, that are better when compared with the model without transformation. To treat time series that exhibit periodic in the correlation function we defined three extensions for periodic autoregressive model, called generalized normal periodic autoregressive model, generalized log-normal periodic autoregressive model and Box-Cox generalized normal periodic autoregressive model. We can observed that the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants have periodic correlation. We present two applications of periodic models from these series. In the models, we note that is not necessary the use of generalized normal distribution in every months, just in some the generalized normal distribution presented better results than the normal distribution. Finally, we define the generalized normal zero inflated distribution and the generalized normal zero inflated ARMA model for time series. Adopting the model for series that have zero inflation and the maximum likelihood method for estimation of parameters, we analyze the serie of the amount of rainfall in the city of São Carlos. |
id |
SCAR_a4c52d8aaa3782f3d67f094c60a8ea51 |
---|---|
oai_identifier_str |
oai:repositorio.ufscar.br:ufscar/7943 |
network_acronym_str |
SCAR |
network_name_str |
Repositório Institucional da UFSCAR |
repository_id_str |
4322 |
spelling |
Milani, Eder AngeloAndrade Filho, Marinho Gomes dehttp://lattes.cnpq.br/4126245980112687http://lattes.cnpq.br/1420630122459706a0716210-408e-4a1d-a4e8-55a0da76bc832016-10-20T13:52:00Z2016-10-20T13:52:00Z2016-03-23MILANI, Eder Angelo. Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada. 2016. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7943.https://repositorio.ufscar.br/handle/ufscar/7943From the generalized normal distribution and concepts of the generalized autoregressive moving averages models we introduce the generalized normal-ARMA model as an alternative way to model time series exhibiting symmetry and tails that may be lighter or heavier when compared the normal distribution. We present application for proposed model using three time series in the hydrology, economy and publics policy areas. The proposed model is presented as good alternative when compared to ARMA model with normal distribution. We extended this model the case of the asymmetric time series. In this case we used the Box-Cox transformation, denoted by Box-Cox generalized normal ARMA. The particular case, when we use the logarithmic transformation is called generalized log-normal ARMA. We adjusted the models with transformation to the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants. We obtain the prediction values for the model with transformation, that are better when compared with the model without transformation. To treat time series that exhibit periodic in the correlation function we defined three extensions for periodic autoregressive model, called generalized normal periodic autoregressive model, generalized log-normal periodic autoregressive model and Box-Cox generalized normal periodic autoregressive model. We can observed that the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants have periodic correlation. We present two applications of periodic models from these series. In the models, we note that is not necessary the use of generalized normal distribution in every months, just in some the generalized normal distribution presented better results than the normal distribution. Finally, we define the generalized normal zero inflated distribution and the generalized normal zero inflated ARMA model for time series. Adopting the model for series that have zero inflation and the maximum likelihood method for estimation of parameters, we analyze the serie of the amount of rainfall in the city of São Carlos.A partir da distribuição normal generalizada e dos conceitos do modelo autorregressivo e de médias móveis generalizado, introduzimos o modelo normal generalizada- ARMA, como alternativa para modelar séries temporais, que exibem simetria e caudas mais leves ou mais pesadas quando comparadas com a distribuição normal. Apresentamos aplicações do modelo proposto, usando três séries temporais, das áreas de hidrologia, políticas públicas e economia. O modelo proposto se apresentou como uma boa alternativa ao modelo ARMA com distribuição normal. Estendemos o modelo para o caso de séries que apresentam assimetria. Neste caso, utilizamos a transformação de Box-Cox, denotado por Box-Cox normal generalizada-ARMA. O caso particular quando utilizamos a transformação logarítmica é chamado de log-normal generalizada-ARMA. Ajustamos os modelos com transformação à séries de vazões das usinas hidrelétricas de Furnas e Sobradinho. Calculamos predições, que para o modelo com transformação, foram melhores, quando comparado ao modelo sem transformação. Com o objetivo de tratar séries que apresentam periodicidade na função de correlação, definimos três extensões do modelo autorregressivo periódico, chamando-os de modelo normal generalizada autorregressivo periódico, modelo log-normal generalizada autorregressivo periódico e modelo Box-Cox normal generalizada autorregressivo periódico. Constatamos que as séries de vazões das usinas hidrelétricas de Furnas e Sobradinho apresentam correlação periódica. Apresentamos duas aplicações dos modelos periódicos propostos usando estas séries. Nos ajustes dos modelos, notamos que não há necessidade da utilização da distribuição normal generalizada em todos os meses, mas em alguns a distribuição normal generalizada se sobressaiu em relação a distribuição normal. Por último, definimos a distribuição normal generalizada zero inflacionada e o modelo para séries temporais normal generalizada zero inflacionada-ARMA. Adotando o método de máxima verossimilhança e o modelo para séries que apresentam inflação de zeros, analisamos a série da quantidade de precipitação pluviométrica da cidade de São Carlos.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Estatística - PPGEsUFSCarModelo Normal Generalizada-ARMAModelo Box-Cox Normal Generalizada-ARMAModelo Normal Generalizada-PAR.Generalized normal ARMA modelBox Cox Generalized Normal ARMA ModelBox-Cox Generalized Normal PAR ModelGeneralized Normal Zero Inflated ARMA ModelCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOSModelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizadainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnline6006006105a248-1b18-49f6-bbf3-c4006673f34ainfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseEAMms.pdfTeseEAMms.pdfapplication/pdf1490434https://repositorio.ufscar.br/bitstream/ufscar/7943/1/TeseEAMms.pdfe7a807666b453630ffb423774d2539b9MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/7943/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTeseEAMms.pdf.txtTeseEAMms.pdf.txtExtracted texttext/plain254758https://repositorio.ufscar.br/bitstream/ufscar/7943/3/TeseEAMms.pdf.txt3b840404a1e3e90865ee9a1217e38e75MD53THUMBNAILTeseEAMms.pdf.jpgTeseEAMms.pdf.jpgIM Thumbnailimage/jpeg5004https://repositorio.ufscar.br/bitstream/ufscar/7943/4/TeseEAMms.pdf.jpga4e7c933ee0c6d4dc65b767f40191574MD54ufscar/79432023-09-18 18:30:59.717oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:30:59Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
title |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
spellingShingle |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada Milani, Eder Angelo Modelo Normal Generalizada-ARMA Modelo Box-Cox Normal Generalizada-ARMA Modelo Normal Generalizada-PAR. Generalized normal ARMA model Box Cox Generalized Normal ARMA Model Box-Cox Generalized Normal PAR Model Generalized Normal Zero Inflated ARMA Model CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
title_short |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
title_full |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
title_fullStr |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
title_full_unstemmed |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
title_sort |
Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada |
author |
Milani, Eder Angelo |
author_facet |
Milani, Eder Angelo |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/1420630122459706 |
dc.contributor.author.fl_str_mv |
Milani, Eder Angelo |
dc.contributor.advisor1.fl_str_mv |
Andrade Filho, Marinho Gomes de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4126245980112687 |
dc.contributor.authorID.fl_str_mv |
a0716210-408e-4a1d-a4e8-55a0da76bc83 |
contributor_str_mv |
Andrade Filho, Marinho Gomes de |
dc.subject.por.fl_str_mv |
Modelo Normal Generalizada-ARMA Modelo Box-Cox Normal Generalizada-ARMA Modelo Normal Generalizada-PAR. |
topic |
Modelo Normal Generalizada-ARMA Modelo Box-Cox Normal Generalizada-ARMA Modelo Normal Generalizada-PAR. Generalized normal ARMA model Box Cox Generalized Normal ARMA Model Box-Cox Generalized Normal PAR Model Generalized Normal Zero Inflated ARMA Model CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
dc.subject.eng.fl_str_mv |
Generalized normal ARMA model Box Cox Generalized Normal ARMA Model Box-Cox Generalized Normal PAR Model Generalized Normal Zero Inflated ARMA Model |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::ANALISE DE DADOS |
description |
From the generalized normal distribution and concepts of the generalized autoregressive moving averages models we introduce the generalized normal-ARMA model as an alternative way to model time series exhibiting symmetry and tails that may be lighter or heavier when compared the normal distribution. We present application for proposed model using three time series in the hydrology, economy and publics policy areas. The proposed model is presented as good alternative when compared to ARMA model with normal distribution. We extended this model the case of the asymmetric time series. In this case we used the Box-Cox transformation, denoted by Box-Cox generalized normal ARMA. The particular case, when we use the logarithmic transformation is called generalized log-normal ARMA. We adjusted the models with transformation to the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants. We obtain the prediction values for the model with transformation, that are better when compared with the model without transformation. To treat time series that exhibit periodic in the correlation function we defined three extensions for periodic autoregressive model, called generalized normal periodic autoregressive model, generalized log-normal periodic autoregressive model and Box-Cox generalized normal periodic autoregressive model. We can observed that the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants have periodic correlation. We present two applications of periodic models from these series. In the models, we note that is not necessary the use of generalized normal distribution in every months, just in some the generalized normal distribution presented better results than the normal distribution. Finally, we define the generalized normal zero inflated distribution and the generalized normal zero inflated ARMA model for time series. Adopting the model for series that have zero inflation and the maximum likelihood method for estimation of parameters, we analyze the serie of the amount of rainfall in the city of São Carlos. |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-10-20T13:52:00Z |
dc.date.available.fl_str_mv |
2016-10-20T13:52:00Z |
dc.date.issued.fl_str_mv |
2016-03-23 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
MILANI, Eder Angelo. Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada. 2016. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7943. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/7943 |
identifier_str_mv |
MILANI, Eder Angelo. Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada. 2016. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7943. |
url |
https://repositorio.ufscar.br/handle/ufscar/7943 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
6105a248-1b18-49f6-bbf3-c4006673f34a |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Estatística - PPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
instname_str |
Universidade Federal de São Carlos (UFSCAR) |
instacron_str |
UFSCAR |
institution |
UFSCAR |
reponame_str |
Repositório Institucional da UFSCAR |
collection |
Repositório Institucional da UFSCAR |
bitstream.url.fl_str_mv |
https://repositorio.ufscar.br/bitstream/ufscar/7943/1/TeseEAMms.pdf https://repositorio.ufscar.br/bitstream/ufscar/7943/2/license.txt https://repositorio.ufscar.br/bitstream/ufscar/7943/3/TeseEAMms.pdf.txt https://repositorio.ufscar.br/bitstream/ufscar/7943/4/TeseEAMms.pdf.jpg |
bitstream.checksum.fl_str_mv |
e7a807666b453630ffb423774d2539b9 ae0398b6f8b235e40ad82cba6c50031d 3b840404a1e3e90865ee9a1217e38e75 a4e7c933ee0c6d4dc65b767f40191574 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR) |
repository.mail.fl_str_mv |
|
_version_ |
1813715567019819008 |