Alvaro Veiga

A hybrid linear-neural model for time series forecasting

This paper considers a linear model with time varying parameters controlled by a neural network to analyze and forecast nonlinear time series.We show that this formulation, called neural coefficient smooth transition autoregressive (NCSTAR) model, is in close relation to the threshold autoregressive (TAR) model and the smooth transition autoregressive (STAR) model with the advantage of naturally incorporating linear multivariate thresholds and smooth transitions between regimes. In our proposal, the neuralnetwork output is used to induce a partition of the input space, with smooth and multivariate thresholds. This also allows the choice of good initial values for the training algorithm.

Modeling Multiple Regimes In Financial Volatility With A Flexible Coefficient Garch(1,1) Model

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

Modeling exchange rates: smooth transitions, neural networks, and linear models

The goal of this paper is to test and model nonlinearities in several monthly exchange rates time series. We apply two different nonlinear alternatives, namely: the artificial neural-network time series model estimated with Bayesian regularization; and a flexible smooth transition specification, called the neuro-coefficient smooth transition autoregression. The linearity test rejects the null hypothesis of linearity in 10 out of 14 series. We compare, using different measures, the forecasting performance of the nonlinear specifications with the linear autoregression and the random walk models.

Diagnostic Checking in a Flexible Nonlinear Time Series Model

This paper considers a sequence of misspecification tests for a flexible nonlinear time series model. The model is a generalization of both the smooth transition autoregressive (STAR) and the autoregressive artificial neural network (AR-ANN) models. The tests are Lagrange multiplier (LM) type tests of parameter constancy against the alternative of smoothly changing ones, of serial independence, and of constant variance of the error term against the hypothesis that the variance changes smoothly between regimes. The small sample behaviour of the proposed tests is evaluated by a Monte-Carlo study and the results show that the tests have size close to the nominal one and a good power.

Design of radial basis function network as classifier in face recognition using eigenfaces

In this paper we investigate alternative designs of a radial basis function network acting as classifier in a face recognition system. The inputs to the RBF network are the projections of a face image over the principal components. A database of 250 facial images of 25 persons is used for training and evaluation. Two RBF designs are studied: the forward selection and the Gaussian mixture model. Both designs are also compared to the conventional Euclidean and Mahalanobis classifiers. A set of experiments evaluates the recognition rate of each method as a function of the number of principal components used to characterize the image samples. The results of the experiments indicate that the Gaussian mixture model RBF achieves the best performance while allowing less neurons in the hidden layer. The Gaussian mixture model approach shows also to be less sensitive to the choice of the training set.

A Combinatorial Approach to Piecewise Linear Time Series Analysis

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.

Tree-structured smooth transition regression models

This paper introduces a tree-based model that combines aspects of classification and regression trees (CART) and smooth transition regression (STR). The model is called the STR-tree. The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analyzed as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on a sequence of Lagrange multiplier (LM) tests of hypotheses. An alternative specification strategy based on a 10-fold cross-validation is also discussed and a Monte Carlo experiment is carried out to evaluate the performance of the proposed methodology in comparison with standard techniques. The STR-tree model outperforms CART when the correct selection of the architecture of simulated trees is discussed. Furthermore, the LM test seems to be a promising alternative to 10-fold cross-validation. Function approximation is also analyzed. When put into proof with real and simulated data sets, the STR-tree model has a superior predictive ability than CART.

Risk constrained contracting strategies of renewable portfolios

The search for clean energy development has motivated the expansion of renewable sources of generation around the world. In Brazil, Small Hydro Plants (SHP), Cogeneration from Sugarcane waste (Biomass) and Wind Power Plants (WPP) are proving themselves to be attractive alternatives over the last years. One important characteristic of each of these technologies is their seasonal availability, which result in financial risks that can make the energy contracting of each individual source too risky: producers are forced to price the market risks faced when selling firm energy contracts (i.e., the risks of purchasing in the spot market whenever their production is smaller than the contracted amount) and this may ultimately lead each of the projects to not being as commercially attractive by itself. On the other hand, in Brazil these sources have complementary energy production patterns, which immediately suggest a portfolio approach to devise energy contracting strategies for Electricity Trading Companies (ETC), which can “blend” these different (and complementary) production patterns to offer a flat and firm energy delivery. The objective of this work is to develop a mathematical model to explore synergies due to the seasonal complementarities of a Biomass, a SHP and a WPP. The proposed model aims at composing an optimal portfolio of these sources and jointly determines the risk-constrained optimal trading strategy for selling an energy contract in the Brazilian forward contract market. The CVaR approach is used to measure and control the market risk associated to the energy delivery. Case studies will be presented with realistic data from the Brazilian power system showing different strategies of commercialization by an ETC.

A high-dimensional VARX model to simulate monthly renewable energy supply

This paper proposes a novel framework for forecasting and simulating renewable energy on a long-term horizon. In this regard, it is presented a monthly multivariate stochastic model for wind and hydro inflow as well as an efficient estimation method for high-dimensional data. Firstly, in order to model the inherent uncertainty of renewable energy supplies, this work proposes a high-dimensional VARX with periodic variance. Secondly, an estimation procedure is suggested based on the maximum likelihood criterion with endogenous variable selection. Due to the presence of multicollinearity and high-dimensionality, the estimation procedure proposed in this work has two main features: (i) a fixed-point algorithm to pursue the maximum likelihood estimators under periodic heteroskedasticity (ii) obtain a sparse solution by means of ℓ1-regularization. Simulations and forecasting results for a real case study involving fifty Brazilian renewable power plants are presented.

Shewhart control charts for dispersion adjusted for parameter estimation

ABSTRACT Several recent studies have shown that the number of Phase I samples required for a Phase II control chart with estimated parameters to perform properly may be prohibitively high. Looking for a more practical alternative, adjusting the control limits has been considered in the literature. We consider this problem for the classic Shewhart charts for process dispersion under normality and present an analytical method to determine the adjusted control limits. Furthermore, we examine the performance of the resulting chart at signaling increases in the process dispersion. The proposed adjustment ensures that a minimum in-control performance of the control chart is guaranteed with a specified probability. This performance is indicated in terms of the false alarm rate or, equivalently, the in-control average run length. We also discuss the tradeoff between the in-control and out-of-control performance. Since our adjustment is based on exact analytical derivations, the recently suggested bootstrap method is no longer necessary. A real-life example is provided in order to illustrate the proposed methodology.