A wavelet model for quasi-periodic signals

• Grant number: 18/26158-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 24, 2019
• End date: April 03, 2019
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Aluísio de Souza Pinheiro
• Grantee: Aluísio de Souza Pinheiro
• Visiting researcher: Paul H.C. Eilers
• Visiting researcher institution: Erasmus University Rotterdam (EUR), Netherlands
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/04654-9 - Time series, wavelets and high dimensional data, AP.TEM

Abstract

Consider a complex-valued signal. Its logarithm can e observed as a two-dimensional time series. The first one represents the signal log-amplitude and the second one, the signal phase. If we suppose a slowly varying set of parameters we have the so-called quasi-periodic signal. Paul Eilers and his collaborators have tackled this problem y spline smoothing. We propose the analysis by wavelet methods. We can foresee the following advantages: coefficient sparsity; computational efficiency; and optimal minimax rates. We are going tio compare the proposed method to several proposals available. Comparisons are going to be done y data analysis, simulation studies and theoretical properties. (AU)