Spatio-temporal models by wavelets

Author(s)

Yangyang Chen

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2023-04-26

Examining board members

Pedro Alberto Morettin; Chang Chiann; Thelma Sáfadi; João Ricardo Sato; Reinaldo Castro de Souza

• Advisor: Pedro Alberto Morettin; Ronaldo Dias

Abstract

The space-time autoregressive moving average model is one of the models that is frequently used in several studies of multivariate time series data. In time series analysis, the assumption of stationarity is important, but it is not always guaranteed in practice and one way to proceed is to consider the locally stationary process. In this thesis we propose a time-varying spatio-temporal model based on the local stationarity assumption. The time-varying parameters are expanded as a linear combination of the wavelet bases and some estimation procedures are used to estimate the coefficients. Some simulations were realized to study the performance of the algorithm and the effects of different types of the spatial weights matrices. And then, an application to historical daily precipitation records of Midwestern states of the USA is illustrated. For the non stationary case, a procedure for estimating the non stationary spatial covariance function for spatio-temporal deformation was proposed. The procedure is based on a monotonic function approach and the functions are expanded using wavelet bases. The deformation proposed guarantees a injective transformation. That is, two distinct locations in the geographic plane are not mapped into the same point in the deformation plane. Finally, some simulations and an application to historical daily maximum temperature records are illustrated. (AU)

• FAPESP's process: 19/05917-6 - New methodologies in deformation of temporal spaces
• Grantee: Yangyang Chen
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)