Modeling of economic time series using automated fuzzy regression methods

Este trabajo se desarrolla en un contexto donde Estadística e Inteligencia Computacional convergen: la Regresión Difusa. La idea fundamental de esta técnica es generalizar conceptos de regresión tradicional a conjuntos difusos. Concretamente, se investigará el potencial de aplicar los métodos automáticos de regresión difusa a cierto tipo de series económicas. En particular, se estudian los siguientes métodos: mínimos cuadrados por lotes, mínimos cuadrados recursivo, aprendizaje desde el ejemplo modificado y agrupamiento difuso combinado. Adicionalmente, se propone el método de mínimos cuadrados recursivo combinado, el cual es una de las principales contribuciones de este trabajo. Cada uno de estos métodos ha sido descrito e implementado en R para el caso unidimensional y se generaliza para el caso de entradas y salidas múltiples. Finalmente, se muestran resultados numéricos de la Reserva Internacional de Libre Disponibilidad y un índice de liquidez financiera, en las cuales se visualiza el comportamiento y desempeño de los métodos comparándolos con modelos SARIMA.Analítika (Revista de Análisis Estadístico), Dirección de Estudios Analíticos Estadísticos (DESAE), Instituto Nacional de Estadística y Censos (INEC

On the Parameter Selection Problem in the Newton-ADI Iteration for Large Scale Riccati Equations

The numerical treatment of linear-quadratic regulator problems for parabolic partial differential equations (PDEs) on infinite time horizons requires the solution of large scale algebraic Riccati equations (ARE). The Newton-ADI iteration is an efficient numerical method for this task. It includes the solution of a Lyapunov equation by the alternating directions implicit (ADI) algorithm in each iteration step. On finite time intervals the solution of a large scale differential Riccati equation is required. This can be solved by a backward differentiation formula (BDF) method, which needs to solve an ARE in each time step. Here, we study the selection of shift parameters for the ADI method. This leads to a rational min-max-problem which has been considered by many authors. Since knowledge about the complete complex spectrum is crucial for computing the optimal solution, this is infeasible for th

Drugs, herbicides, and numerical simulation

The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon

Fourier-Splitting Method for Solving Hyperbolic LQR Problems

We consider the numerical approximation to linear quadratic regulator problems for hyperbolic partial differential equations where the dynamics is driven by a strongly continuous semigroup. The optimal control is given in feedback form in terms of Riccati operator equations. The computational cost relies on solving the associated Riccati equation and computing the optimal state. In this paper we propose a novel approach based on operator splitting idea combined with Fourier’s method to efficiently compute the optimal state. The Fourier’s method allows to accurately approximate the exact flow making our approach computational efficient. Numerical experiments in one and two dimensions show the performance of the proposed method