@article{Garibo-Morante_Ornelas Tellez_2021, title={Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology}, volume={20}, url={https://latamt.ieeer9.org/index.php/transactions/article/view/5321}, abstractNote={<p>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.<br />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.</p>}, number={3}, journal={IEEE Latin America Transactions}, author={Garibo-Morante, Angel Agustin and Ornelas Tellez, Fernando}, year={2021}, month={Jul.}, pages={372–378} }