Spatio-temporal models by wavelets

• Ano de defesa: 2023
• Autor(a) principal: Chen, Yangyang
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Espaço-temporal; Filtro de Kalman; Função de covariância espacial; Kalman filter; Locally stationary processes; Non stationary processes; Ondaletas; Processos localmente estacionários; Processos não estacionários; Spatial covariance function; Spatio-temporal; Time-varying; Variante no tempo; Wavelets
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-25052023-222701/

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.