Time series decomposition preserving deterministic influences

• Grant number: 14/21636-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2015
• End date: July 10, 2016
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Rodrigo Fernandes de Mello
• Grantee: Felipe Simões Lage Gomes Duarte
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

With technological developments, it has become possible to collect and model large amounts of data produced over time. These data are typically generated by industrial processes, human operations or natural phenomena. By modeling them, we can understand, predict and observe their changes as well as control them. Overall, these data are formed by deterministic and stochastic components. When modeling such data by considering only one of the components, we can draw incomplete or erroneous conclusions. The ideal scenario relies on both approaches, each one applied on its respective influence, i.e., by employing Statistical tools on the stochastic component, and Dynamical System tools on the deterministic one. This requires the decomposition of time series into two influences. Current decomposition approaches lack in terms of the type of series they can model as well as the bias they impose in the decomposition step. Consequently, they produce incorrect deterministic components, jeopardizing modeling and prediction results. In this context, this PhD project is proposed to employ concepts of mathematical topology to preserve the deterministic influences of time series during decomposition. Therefore, we expect to improve time series modeling and prediction. This proposal will be compared against the most prominent from literature. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DUARTE, FELIPE S. L. G.; RIOS, RICARDO A.; HRUSCHKA, EDUARDO R.; DE MELLO, RODRIGO F.. Decomposing time series into deterministic and stochastic influences: A survey. DIGITAL SIGNAL PROCESSING, v. 95, DEC 2019. (17/16548-6, 13/07375-0, 14/21636-3)

DUARTE, FELIPE S. L. G.; RIOS, RICARDO A.; HRUSCHKA, EDUARDO R.; DE MELLO, RODRIGO F.; IEEE. Time Series Decomposition Using Spring System Applied on Phase Spaces. 2018 7TH BRAZILIAN CONFERENCE ON INTELLIGENT SYSTEMS (BRACIS), v. N/A, p. 6-pg., 2018-01-01. (13/07375-0, 14/21636-3, 17/16548-6)

DA COSTA, FAUSTO G.; DUARTE, FELIPE S. L. G.; VALLIM, ROSANE M. M.; DE MELLO, RODRIGO F.. Multidimensional surrogate stability to detect data stream concept drift. EXPERT SYSTEMS WITH APPLICATIONS, v. 87, p. 15-29, NOV 30 2017. (14/21636-3, 14/13323-5)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

DUARTE, Felipe Simões Lage Gomes. Time series decomposition while preserving deterministic influences. 2020. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.