Wavelet estimation of functional coefficient regression models

Autor(es)

Montoril, Michel H. ^[1] ; Morettin, Pedro A. ^[2] ; Chiann, Chang ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Juiz de Fora, Inst Exact Sci, Dept Stat, Juiz De Fora - Brazil

^[2] Univ Sao Paulo, Inst Math & Stat, Dept Stat, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING; v. 16, n. 1 JAN 2018.
• Citações Web of Science: 0

Resumo

The area of nonlinear time series models has experienced a great development since the 1980s. Although there is a wide range of parametric nonlinear time series models, in general, we do not know if the postulated model is the most appropriated one for a specific data set. This situation highlights the importance of nonparametric models. An interesting nonparametric model to fit nonlinear time series is the well-known functional coefficient regression model. Nonparametric estimations by, e.g., local linear regression and splines, are developed in the literature. In this work, we study the estimation of such a model using wavelets. It is a proposal that takes into account both, classical and warped wavelets. We present the rates of convergence of the proposed estimators and carry out simulation studies to evaluate automatic procedures (among AIC, AICc and BIC) for selecting the coarsest and finest levels to be used during the estimation process. Moreover, we illustrate the methodology with an application to a real data set, where we also calculate multi-step-ahead forecasts and compare the results with other methods known in the literature. (AU)

• Processo FAPESP: 13/21273-5 - Estimação de modelos de regressão linear semifuncionais via ondaletas
• Beneficiário: Michel Helcias Montoril
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 13/09035-1 - Modelos de regressão para dados funcionais
• Beneficiário: Michel Helcias Montoril
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 08/51097-6 - Séries temporais, análise de dependência e aplicações
• Beneficiário: Pedro Alberto Morettin
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/00506-1 - Séries temporais, ondaletas e análise de dados funcionais
• Beneficiário: Pedro Alberto Morettin
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 09/09588-5 - Estimação de modelos FAR (univariados e multivariados) via ondaletas
• Beneficiário: Michel Helcias Montoril
• Modalidade de apoio: Bolsas no Brasil - Doutorado