Functional-coefficient regression models for time series

Author(s)

Michel Helcias Montoril

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2013-02-28

Examining board members

Pedro Alberto Morettin; Chang Chiann; Ronaldo Dias; Aluísio de Souza Pinheiro; João Ricardo Sato

• Advisor: Pedro Alberto Morettin; Chang Chiann

Abstract

In this thesis, we study about fitting functional-coefficient regression models for time series, by splines, wavelets and warped wavelets. We consider models with independent and correlated errors. Through the three estimation approaches, we obtain rates of convergence to zero for average distances between the functions of the model and their estimators proposed in this work. In the case of (warped) wavelets approach, we also obtain asymptotic results in more specific situations, in which the functions of the model belong to Sobolev and Besov spaces. Moreover, Monte Carlo simulation studies and applications to real data sets are presented. Through these numerical results, we make comparisons between the three estimation approaches proposed here and comparisons between other approaches known in the literature, where we verify interesting performances in the sense that the proposed approaches provide competitive results compared to the results from methodologies used in literature. (AU)

• FAPESP's process: 09/09588-5 - Estimation of FAR models by wavelets
• Grantee: Michel Helcias Montoril
• Support Opportunities: Scholarships in Brazil - Doctorate