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| Author(s): |
Felipe Simões Lage Gomes Duarte
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2020-01-13 |
| Examining board members: |
Eduardo Raul Hruschka;
Rafael Izbicki;
Francisco Aparecido Rodrigues;
Diego Furtado Silva
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| Advisor: | Rodrigo Fernandes de Mello; Eduardo Raul Hruschka |
| Abstract | |
Technological advances allowed to collect and model large scales of data produced along time by industrial, human and natural phenomena. In terms of time series, such data are composed of deterministic, solely based on past observations or associated to recurrent events, and stochastic influences, due to random effects. Models using only one of those influences tend to produce suboptimal and incomplete results. Therefore, one should ideally model the stochastic component using Statistical tools and the deterministic one with Dynamical Systems. This scenario leads us to the decomposition of time series in attempt to obtain more accurate models and best prediction results. Several approaches have been applied to address such decomposition stage, including: (i) Fourier Transform; (ii) Wavelet Transform; (iii) Moving Average; (iv) Singular Spectrum Analysis; (v) Lazy; (vi) GHKSS; and (vii) other approaches based on the Empirical Mode Decomposition (EMD). Those approaches have drawbacks related to the bias imposed by their respective sets of admissible functions, having the sinusoidal as the typical to represent the deterministic component extracted, thus loosing the original time series bias, what leads to sub-optimal models and insatisfactory prediction results. In this context, this PhD thesis introduces three time series decompositions approaches that aim to preserve as much as possible the deterministic influences by using phase-spaces, what helps maintaining the original data bias, to mention: (i) Spring, (ii) Spring Time Domain e (iii) Spring*. Those approaches were experimentally assessed and compared against the state-of-the-art through measurements commonly used in the literature, more precisely: Mean Absolute Error (MAE) and Mean Distance from Diagonal Line (MDDL). Spring and its variations confirmed to be more effective to separate deterministic and stochastic influences, thus improving the modeling and prediction processes. At last, the proposed decomposition approaches were plugged into the polynomial and the radial basis function prediction techniques to confirm the hypothesis that the forecasting of series observations could be more accurate what was corroborated given errors were overall reduced. (AU) | |
| FAPESP's process: | 14/21636-3 - Time series decomposition preserving deterministic influences |
| Grantee: | Felipe Simões Lage Gomes Duarte |
| Support Opportunities: | Scholarships in Brazil - Doctorate |