Ochoa Tapia, Ysela

Profile Picture

Filters

20141
Reset filters

Settings

Citations

Publication Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Publication
    Técnica de componentes indepedientes: aplicación y análisis de datos de series temporales sobre Puerto Rico
    (2014-06) Ochoa Tapia, Ysela; Lorenzo González, Edgardo; College of Arts and Sciences - Sciences; Rivera Marrero, Olgamary; Santana Morant, Dámaris; Department of Mathematics; Santana Rorant, Dámaris
    The time series analysis is oriented to the problem of prediction. Perform a univariate analysis is simpler than a multivariate analysis because the univariate analysis is concerned only with the structure of internal dependency of a series, while the multivariate analysis also considers the dependency between series and its combinations. In this research we present a method for the prediction of multivariate time series, using its independent latent series, obtained through the independent component analysis as a blind source separation technique. The fact that the latent series are independent, allow us to reduce the multivariate analysis to a multiple univariate one. Formally, the independent component analysis, is a mixture model of random va- riables X = AS, where the theory developed is focused on estimating the mixing matrix A and the latent sources S, under assumptions that the matrix A is full range, and the sources S are independent non-Gaussian [12]. In this thesis, we have temporal data in form of time series, where the model of independent components will be a combination of latent series as X(t) = AS(t), where t is time. The estimation is based on the only available information X(t), that as a result of being time series data, there is no restriction on the data being Gaussian or not [11]. The model does not incorporates errors, because it assumes white noise. To perform the estimation of latent series various methods have been developed, from different points of view, based on the hypothesis that the latent series have a certain temporal structure associated with different autocorrelation functions [6]. These methods are called temporal-space decorrelation. The most commonly used algorithms are AMUSE based on whitening of data and the covariance matrix of a time delay [23] and SOBI based on second order blind identification, such that diagonalizes joint covariance matrices of a fixed number of time delays [1]. After the estimation of the latent series, the methodology proposed by Box and Jenkins is used, through SARIMA models [2], for forecast each latent series independently. Then under the model of independent components X(t) = AS(t) with the predictions of the latent series S(t + h), we predict the original time series X(t + h). The methodology has been applied to multivariate time series of electricity consumption and the consumer index price of Puerto Rico, economic indicators that are key for decision making and economy of Puerto Rico [7]; for the development of methodology we use the AMUSE and SOBI algorithms. The results show the efficiency of the methodology and the reduction of the complexity of the prediction problem.