Miguel Pasadas

Soft-computing techniques and ARMA model for time series prediction

The challenge of predicting future values of a time series covers a variety of disciplines. The fundamental problem of selecting the order and identifying the time varying parameters of an autoregressive moving average model (ARMA) concerns many important fields of interest such as linear prediction, system identification and spectral analysis. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. This study was designed: (a) to investigate a hybrid methodology that combines ANN and ARMA models; (b) to resolve one of the most important problems in time series using ARMA structure and Box-Jenkins methodology: the identification of the model. In this paper, we present a new procedure to predict time series using paradigms such as: fuzzy systems, neural networks and evolutionary algorithms. Our goal is to obtain an expert system based on paradigms of artificial intelligence, so that the linear model can be identified automatically, without the need of human expert participation. The obtained linear model will be combined with ANN, making up an hybrid system that could outperform the forecasting result.

Hybridization of intelligent techniques and ARIMA models for time series prediction

Traditionally, the autoregressive moving average (ARMA) model has been one of the most widely used linear models in time series prediction. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional ARMA structure. These linear models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. In this paper we propose a hybridization of intelligent techniques such as ANNs, fuzzy systems and evolutionary algorithms, so that the final hybrid ARIMA-ANN model could outperform the prediction accuracy of those models when used separately. More specifically, we propose the use of fuzzy rules to elicit the order of the ARMA or ARIMA model, without the intervention of a human expert, and the use of a hybrid ARIMA-ANN model that combines the advantages of the easy-to-use and relatively easy-to-tune ARIMA models, and the computational power of ANNs.

Approximation by discrete variational splines

In this paper we present a numerical approximation of curves and surfaces from a given scattered data set. An approximating curve or surface problem is obtained by minimizing a quadratic functional in a parametric finite element space, its solution is called a discrete smoothing variational spline. The existence and uniqueness of this problem are shown, as long as the convergence of the method is established. Finally some particular examples are given.

Smoothing variational splines

Abstract This paper deals with the problem of constructing some free-form curves and surfaces from given Lagrangian and/or Hermite data. We define the smoothing variational spline function by minimizing a certain quadratic functional in a Sobolev space and establish the convergence of the associated method.

Approximation of surfaces by fairness bicubic splines

In this paper we present an approximation method of surfaces by a new type of splines, which we call fairness bicubic splines, from a given Lagrangian data set. An approximating problem of surface is obtained by minimizing a quadratic functional in a parametric space of bicubic splines. The existence and uniqueness of this problem are shown as long as a convergence result of the method is established. We analyze some numerical and graphical examples in order to prove the validity of our method.

Variational bivariate interpolating splines with positivity constraints

This paper deals with a shape preserving method of interpolating positive data at points of the plane in R2. We formulate a problem in order to define a positive interpolation variational spline in the Sobolev space Hm (Ω), where Ω is a non-empty bounded set of R2, by minimizing the semi-norm of order m, and we discrete such problem in a finite element space. An algorithm allows us to compute the resulting function. Some convergence theorems are established. The error is of the order O(1/N)m when N tends to +∞, being N the number of the interpolating points. Some numerical and graphical examples are given in order to test the validity of this method.

Approximation by shape preserving interpolation splines

In this paper we present a shape preserving method of interpolation for scattered data defined in the form of some constraints such as convexity, monotonicity and positivity. We define a k-convex interpolation spline function in a Sobolev space, by minimizing a semi-norm of order k + 1, and we discretize it in the space of piecewise polynomial spline functions. The shape preserving condition that we consider here is the positivity of the derivative function of order k. We present an algorithm to compute the resulting function and we show its convergence. Some convergence theorems are established. The error is of order o(1/N) k+1 ,w hereN is the number of the Lagrangian data. Finally, we analyze some numerical and graphical examples.  2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

Construction of ODE curves

This paper deals with a construction problem of free-form curves from data constituted by some approximation points and a boundary value problem for an ordinary differential equation (ODE). The solution of this problem is called an ODE curve. We discretize the problem in a space of B-spline functions. Finally, we analyze a graphical example in order to illustrate the validity and effectiveness of our method.

Spline approximation of discontinuous multivariate functions from scattered data: 281

Abstract The approximation of discontinuous multivariate functions from a set of scattered data points is usually a two-stage process: first, a detection algorithm is applied to localize the discontinuity sets, then the functions are reconstructed using a fitting method. In this paper we propose a new method for the second stage, based on the computation of discrete smoothing Dm-splines. We establish a result of local convergence of the approximations provided by the method. Finally, we give some numerical and graphical examples.

Optimization of parameters for curve interpolation by cubic splines

In this paper, we present an interpolation method for curves from a data set by means of the optimization of the parameters of a quadratic functional in a space of parametric cubic spline functions. The existence and the uniqueness of this problem are shown. Moreover, a convergence result of the method is established in order to justify the method presented. The aforementioned functional involves some real non-negative parameters; the optimal parametric curve is obtained by the suitable optimization of these parameters. Finally, we analyze some numerical and graphical examples in order to show the efficiency of our method.