André Luis Santiago Maia

Forecasting models for interval-valued time series

This paper presents approaches to interval-valued time series forecasting. The first and second approaches are based on the autoregressive (AR) and autoregressive integrated moving average (ARIMA) models, respectively. The third approach is based on an artificial neural network (ANN) model and the last is based on a hybrid methodology that combines both ARIMA and ANN models. Each approach fits, respectively, two models on the mid-point and range of the interval values assumed by the interval-valued time series in the learning set. The forecasting of the lower and upper bounds of the interval value of the time series is accomplished through a combination of forecasts from the mid-point and range of the interval values. The evaluation of the models presented is based on the estimation of the average behavior of the mean absolute error and mean squared error in the framework of a Monte Carlo experiment. The results demonstrate that the approaches are useful in forecasting alternatives for interval-valued time series and indicate that the hybrid model is an effective way to improve the forecasting accuracy achieved by any one of the models separately.

Dinâmica inflacionária brasileira: resultados de auto-regressão quantílica

Neste artigo nos estudamos a dinâmica inflacionaria brasileira apos a implementacao do Plano Real em 1994. Nos usamos modelos auto-regressivos quantilicos e testes de raiz unitaria baseados em representacoes auto-regressivas quantilicas para caracterizar tal dinâmica. O artigo mostra que a dinâmica inflacionaria nao apresenta comportamento uniforme ao longo dos diferentes quantis condicionais. Em particular, os resultados fornecem evidencia de dinâmica globalmente estacionaria, mesmo com o processo alcancando nao-estacionariedade na cauda superior da distribuicao condicional.

Hybrid model with dynamic architecture for forecasting time series

Nonlinear artificial neural network models are very attractive for modeling and forecasting time series. The use of such models in these types of applications is motivated by experimental results that show a high capacity of approximation for functions with high accuracy. However, many researchers have used feedforward and/or backpropagation models for time series predictions. In this paper, a model is applied for neural networks with the dynamic architecture proposed by Ghiassi and Saidane (2005), known as the DAN2 model. The results of DAN2 are compared with auto-regressive integrated mobile average (ARIMA) models. As the main result of the paper, we propose a hybrid model with dynamic architecture (HAD) based on combinations of individual forecasts from the DAN2 and ARIMA models with the aim of obtaining more precise forecasts for poorly behaved time series. The results suggest that for this kind of series, the HAD hybrid model outperforms the individual DAN2 and ARIMA models.

Fitting a Least Absolute Deviation Regression Model on Interval-Valued Data

This paper introduces a least absolute deviation (LAD) regression model suitable for manage interval-valued data. Each example of the data set is described by a feature vector where each feature value is an interval. In the approach, it is fitted two LAD regressions, respectively, on the mid-point and range of the interval values assumed by the variables. The prediction of the lower and upper bound of the interval value of the dependent variable is accomplished from its mid-point and range which are estimated from the fitted LAD regression models applied to the mid-point and range of each interval values of the independent variables. The evaluation of the proposed prediction method is based on the estimation of the average behaviour of root mean squared error and of the correlation coefficient in the framework of a Monte Carlo experience in comparison with the method proposed in [5].

Symbolic interval time series forecasting using a hybrid model

This paper presents two approaches to symbolic interval time series forecasting. The first approach is based on the autoregressive moving average (ARMA) model and the second is based on a hybrid methodology that combines both ARMA and artificial neural network (ANN) models. In the proposed approaches, two models are respectively fitted to the mid-point and range of the interval values assumed by the symbolic interval time series in the learning set. The forecast of the lower and upper bounds of the interval value of the time series is accomplished through the combination of forecasts from the mid-point and range of the interval values. The evaluation of the proposed models is based on the estimation of the average behaviour of the mean absolute error and mean square error in the framework of a Monte Carlo experiment.

A hybrid model for symbolic interval time series forecasting

This paper presents two approaches to symbolic interval time series forecasting. The first approach is based on the autoregressive moving average (ARMA) model and the second is based on a hybrid methodology that combines both ARMA and artificial neural network (ANN) models. In the proposed approaches, two models are respectively fitted to the mid-point and range of the interval values assumed by the symbolic interval time series in the learning set. The forecast of the lower and upper bounds of the interval value of the time series is accomplished through the combination of forecasts from the mid-point and range of the interval values. The evaluation of the proposed models is based on the estimation of the average behaviour of the mean absolute error and mean square error in the framework of a Monte Carlo experiment.

Neural Networks and Exponential Smoothing Models for Symbolic Interval Time Series Processing Applications in Stock Market

The need to consider data that contain information that cannot be represented by classical models has led to the development of symbolic data analysis (SDA). As a particular case of symbolic data, symbolic interval time series are interval-valued data which are collected in a chronological sequence through time. This paper presents two approaches to symbolic interval time series analysis. The first approach is based on artificial neural networks. The second, is a new model based on exponential smoothing methods, where the smoothing parameters are estimated by using techniques for nonlinear optimization problems with bound constraints. The practicality of the methods is demonstrated by applications on real interval time series.

Exponential smoothing methods for forecasting bar diagram-valued time series

When a set of categories with related frequencies of the observed variable is available for each time point we have a bar diagram-valued time series. This paper introduces exponential smoothing methods to forecast bar diagram-valued time series data. The proposed method is inspired in the approach introduced by Maia and De Carvalho (2011) to deal with inteval-valued time series. The smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The results are discussed based on two wellknown classical performance measurements, which have been adapted here for this particular type of data: the U of Theil statistics and average relative variance (ARV) in the framework of a Monte Carlo experiment. The synthetic data sets take into account differents aspects, e.g., sample size and forecast horizons among others. Applications using real bar diagram-valued time series also were considered to demonstrate the practicality of the methods. The results demonstrate that the proposed approaches are useful in forecasting bar diagram-valued times series.