Improving time series modeling by decomposing and analysing stochastic and deterministic influences - Rios, Ricardo Araújo (2013)
This thesis presents a study on time series analysis, which was conducted based on the following hypothesis: time series influenced by additive noise can be decomposed into stochastic and deterministic components in which individual models permit obtaining a hybrid one that improves accuracy. This hypothesis was confirmed in two steps. In the first one, we developed a formal analysis using the Nyquist-Shannon sampling theorem, proving Intrinsic Mode Functions (IMFs) extracted from the Empirical Mode Decomposition (EMD) method can be combined, according to their frequency intensities, to form stochastic and deterministic components. Considering this proof, we designed two approaches to decompose time series, which were evaluated in synthetic and real-world scenarios. Experimental results confirmed the importance of decomposing time series and individually modeling the deterministic and stochastic components, proving the second part of our hypothesis. Furthermore, we noticed the individual analysis of both components plays an important role in detecting patterns and extracting implicit information from time series. In addition to these approaches, this thesis also presents two new measurements. The first one is used to evaluate the accuracy of time series modeling in forecasting observations. This measurement was motivated by the fact that existing measurements only consider the perfect match between expected and predicted values. This new measurement overcomes this issue by also analyzing the global time series behavior. The second measurement presented important results to assess the influence of the deterministic and stochastic components on time series observations, supporting the decomposition process. Finally, this thesis also presents a Systematic Literature Review, which collected important information on related work, and two new methods to produce surrogate data, which permit investigating the presence of linear and nonlinear Gaussian processes in time series, irrespective of the influence of nonstationary behavior