Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology



Signal modeling, Time series, Optimal observer, Kalman-Bucy filter, Forecast, Fourier series


This paper contributes by developing an univariate and multivariate harmonic decomposition methodology to model time series.The models are stated in a state space representation derived from a Fourier series analysis to describe an arbitrary signal. The frequency values of the harmonic content are used to define state variables in order to describe a signal through a time-varying linear state space model, which serves to synthesize an optimal state observer (Kalman-Bucy filter). Once the observer converges and the states (harmonics) become constant, the observer model can be used to predict the signal, i.e., a time series forecasting can be performed.
The preocedure can be developed for the univariate or multivariate case of time series modeling, where in the last one, a statistical analysis is used to determine which variables should be taken into account to obtain a more accurate model. The proposed modeling approach is successfully applied for the modeling and forecast of the time series of electrical power demand and a wind/solar profile.


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Author Biographies

Angel Agustin Garibo-Morante, Universidad Michoacana de San Nicolas de Hidalgo

Received the B. Sc. and M.Sc. degree in electrical engineering from the Universidad Michoacana de San Nicolas de Hidalgo (UMSNH), Morelia, Mexico in 2017 and 2020, respectively. His research interests are nonlinear control, applied control, signal processing and modeling, forecasting, robotics, microcontrollers, artificial neural networks, diffusion logic, and IoT.

Fernando Ornelas Tellez, Universidad Michoacana de San Nicolas de Hidalgo

Received the B.Sc. degree from the Instituto Tecnologico de Morelia (ITM), Mexico, in 2005 and the M.Sc. and D.Sc. degrees in electrical engineering from the Advanced Studies and Research Center, National Polytechnic Institute (CINVESTAV-IPN), Guadalajara, Mexico, in 2008 and 2011, respectively.
His research interests are dynamical system modeling, neural control, optimal control, electrical machines, and power electronics.


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How to Cite

Garibo-Morante, A. A., & Ornelas Tellez, F. (2021). Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology. IEEE Latin America Transactions, 20(3), 372–378. Retrieved from https://latamt.ieeer9.org/index.php/transactions/article/view/5321