Improving time series modeling by decomposing and analyzing stochastic and deterministic influences

• Published in: Signal processing 2013-11, Vol.93 (11), p.3001-3013
• Main Authors: Rios, Ricardo Araújo, de Mello, Rodrigo Fernandes
• Format: Article
• Language: English
• Subjects: Adjustment; Applied sciences; Decomposition; Detection, estimation, filtering, equalization, prediction; Deterministic component; Empirical analysis; Empirical mode decomposition; Exact sciences and technology; Information, signal and communications theory; Recurrence plot; Signal and communications theory; Signal processing; Signal, noise; Stochastic component; Stochasticity; Telecommunications and information theory; Time series; Time series analysis; Time series decomposition
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.04.017

This paper proposes a new approach to improve time series modeling by considering stochastic and deterministic influences. Assuming such influences are present in observations, a first decomposition step is required to split them into two components: one stochastic and another deterministic. As second step, models are adjusted on each component and combined to form a hybrid model improving time series analysis. The proposed approach considers the Empirical Mode Decomposition method and a Recurrence Plot-based measurement to decompose and assess stochastic and deterministic influences. Experiments confirmed improvements in time series modeling. •We present an approach to decompose time series into components.•The obtained components allow understanding stochastic and deterministic influences.•By knowing such influences we can estimate models with high accuracy.•A new measure evaluates the behavior of the predicted and expected observations.•Experiments confirmed improvements by modeling stochastic/deterministic influences.