LUIZ FERNANDO CUNHA DUARTE

Data: 13/08/2024, 15:30h

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Título:  SARIMAX.jl: Open-Source Time Series Modeling in Julia through Advanced Optimization

Orientadores: Davi Michel Valladão | PUC-Rio

Resumo:

This dissertation introduces SARIMAX.jl, a Julia package designed for time series estimation. The primary contribution of this work is the dissociation of model formulation from the estimation process, enabling the selection of the most appropriate estimation method for each specific situation. SARIMAX.jl employs advanced optimization techniques to enhance stability, robustness, and accuracy in modeling ARIMA processes. It offers flexibility by allowing users to incorporate regularization and switch objective functions. Through a comparative study, SARIMAX.jl demonstrates superior performance across various metrics, establishing it as a reliable open-source option for time series modeling. Additionally, this dissertation proposes a mixed-integer optimization approach for the specification and estimation of a specific subset of SARIMA models, known as autoregressive integrated (ARI) models. This approach guarantees global optimality in parameter estimation and the specification of the integration order and autoregressive part.