TY - JOUR
AU - Garibo-Morante, Angel Agustin
AU - Ornelas Tellez, Fernando
PY - 2021/07/06
Y2 - 2023/02/02
TI - Univariate and Multivariate Time Series Modeling using a Harmonic Decomposition Methodology
JF - IEEE Latin America Transactions
JA - IEEE LAT AM T
VL - 20
IS - 3
SE - Articles
DO -
UR - https://latamt.ieeer9.org/index.php/transactions/article/view/5321
SP - 372-378
AB - <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>
ER -