Paulo S. G. de Mattos Neto

Correcting and combining time series forecasters

Combined forecasters have been in the vanguard of stochastic time series modeling. In this way it has been usual to suppose that each single model generates a residual or prediction error like a white noise. However, mostly because of disturbances not captured by each model, it is yet possible that such supposition is violated. The present paper introduces a two-step method for correcting and combining forecasting models. Firstly, the stochastic process underlying the bias of each predictive model is built according to a recursive ARIMA algorithm in order to achieve a white noise behavior. At each iteration of the algorithm the best ARIMA adjustment is determined according to a given information criterion (e.g. Akaike). Then, in the light of the corrected predictions, it is considered a maximum likelihood combined estimator. Applications involving single ARIMA and artificial neural networks models for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, and Nasdaq Index series illustrate the usefulness of the proposed framework.

Error modeling approach to improve time series forecasters

Abstract In time series forecasting exercises it has been usual to suppose that the error series generated by the forecasters have a white noise behavior. However, it is possible that such supposition is violated in practice due to model misspecification or disturbances of the phenomenon not captured by the predictive models. It may lead to statistically biased and/or inefficient predictors. The present paper introduces an approach to correct predetermined forecasters by recursively modeling their remaining residuals. Two formalisms are used to illustrate the recursive approach: the well-known (linear) autoregressive integrated moving average (ARIMA) and the (non-linear) Artificial Neural Network (ANN). These models are recursively adjusted to the remaining residuals of a given forecaster until a white noise behavior is achieved. Applications involving ARIMA and ANN forecasters for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, Nasdaq Index, Wolf׳s Sunspot, and Canadian Lynx data series indicate the usefulness of the proposed framework.

Hybrid intelligent system for air quality forecasting using phase adjustment

Abstract The pollution caused by particulate matter (PM) concentration has a negative impact on population health, due to its relationship with several diseases. In this sense, several intelligent systems have been proposed for forecasting the PM concentration. Although it is known in the literature that PM concentration time series behave like random walk, to the authors’ knowledge there is no intelligent systems developed to forecast the PM concentration that consider this characteristic. In this paper, we present an architecture developed to forecast time series guided by random walk process. The architecture, called Time-delay Added Evolutionary Forecasting (TAEF), consists of two steps: parameters optimization and phase adjustment. In the first step, a genetic optimization procedure is employed to adjust the parameters of a Multilayer Perceptron neural network that is used as the prediction model. The genetic algorithm adjusts the following parameters of the prediction model: the number of input nodes (time lags), the number of neurons in the hidden layer and the training algorithm. The second step is performed aiming to reduce the difference between the forecasting and the actual concentration value of the time series, that occur in the forecasting of the time series with random walk behavior. The approach is data-driven and only uses the past values of the pollutant concentrations to predict the next day concentration; in other words, it does not require any exogenous information. The experimental study is performed using time series of concentration levels of particulate matter (PM2.5 and PM10) from Helsinki and shows that the approach overcomes previous state-of-the-art methods by a large margin.

Combining Artificial Neural Network and Particle Swarm System for time series forecasting

Forecasting systems have been widely used for decision making and one of its most promising approaches is based on Artificial Neural Networks (ANN). In this paper, a hybrid swarm system is presented for the time series forecasting problem, which consists of an intelligent hybrid model composed of an ANN combined with Particle Swarm Optimizer (PSO). The proposed method searches the relevant time lags for a correct characterization of the time series, as well as the number of processing units in the hidden layer, the training algorithm and the modeling of ANN. The proposed method shows an efficient procedure to adjust the ANN parameters through the use of a particle swarm optimization mechanism. An experimental analysis is conducted with the proposed method using six real world time series and the results are discussed according to five performance measures.

A prime step in the time series forecasting with hybrid methods: The fitness function choice

Artificial Neural Networks (ANN) have been widely used in order to solve the time series forecasting problem. One of its most promising approaches is the combination with other intelligence techniques, as genetic algorithms, evolutionary strategies, etc. The efficiency of these technics, if used correctly, can be very high. Unfortunately, in terms of fitness function, there is still some lacks of experimental (and theoretical) results to help the practitioners to use these technics in order to find better predictions. This paper proposes others fitness functions (instead of conventional MSE based) and presents an experimental investigation of eight different fitness functions for time series prediction based on five well known measures of statistical performance in the literature. Using a hybrid method for tuning of the ANN structure and parameters (a modified genetic Algorithm), an analysis of the final results effects are made according with four relevant time series. This work shows that small changes of the fitness function evaluation can lead to a significantly improved performance.

Time-series forecasting of pollutant concentration levels using particle swarm optimization and artificial neural networks

This study evaluates the application of an intelligent hybrid system for time-series forecasting of atmospheric pollutant concentration levels. The proposed method consists of an artificial neural network combined with a particle swarm optimization algorithm. The method not only searches relevant time lags for the correct characterization of the time series, but also determines the best neural network architecture. An experimental analysis is performed using four real time series and the results are shown in terms of six performance measures. The experimental results demonstrate that the proposed methodology achieves a fair prediction of the presented pollutant time series by using compact networks.

An intelligent perturbative approach for the time series forecasting problem

In this paper it is introduced a new perturbative approach for time series forecasting. The model uses the error of the series, that is the difference between real value of the series and the output of a predictive method, to improve the series forecasting. The methodology proposed is inspired in the Perturbation Theory, that consists in a set of approximation schemes used to describe a complicated problem in terms of simpler ones. For an experimental investigation, this theory, is combined with the TAEF method, that has interesting results when compared with the literature. This combination is called P-TAEF (Perturbative TAEF). Its results over some time series are discussed and compared with previous results found in the literature. It was used several performance measures that showed the robustness of the perturbative approach.

Measurement of Fitness Function efficiency using Data Envelopment Analysis

Over the last years, Evolutionary Algorithms (EAs) have been proposed aiming to find the best configuration of the Artificial Neural Networks (ANN) parameters. Among several parameters of an EA that can influence the quality of the found solution, the choice of the Fitness Function is the most important for its effectiveness and efficiency, given that different Fitness Functions have distinct fitness landscapes. In other words, the Fitness Function guides the evolutionary process of the candidate solutions according with a given criterion of the performance. However, there is not an universal criterion to identify the best performance measure. Thus, what is the Fitness Function more efficient among a set of several possible options? This paper presents a methodology based on Data Envelopment Analysis (DEA) to find the more efficient Fitness Function among candidates. The DEA is used to determine the best combination of statistical measures to build the more efficient Fitness Function for a EA. The case study employed here consists of a hybrid system composed by Evolutionary Strategy and ANN applied to solve the time series forecasting problem. The data analyzed are composed by financial, agribusiness and natural phenomena. The results show that establishment of the Fitness Function is a crucial point in the EA design, being a key factor to obtain the best solution for a limited number of EAs iteration.

Lag selection for time series forecasting using Particle Swarm Optimization

The time series forecasting is an useful application for many areas of knowledge such as biology, economics, climatology, biology, among others. A very important step for time series prediction is the correct selection of the past observations (lags). This paper uses a new algorithm based in swarm of particles to feature selection on time series, the algorithm used was Frankensteins Particle Swarm Optimization (FPSO). Many forms of filters and wrappers were proposed to feature selection, but these approaches have their limitations in relation to properties of the data set, such as size and whether they are linear or not. Optimization algorithms, such as FPSO, make no assumption about the data and converge faster. Hence, the FPSO may to find a good set of lags for time series forecasting and produce most accurate forecastings. Two prediction models were used: Multilayer Perceptron neural network (MLP) and Support Vector Regression (SVR). The results show that the approach improved previous results and that the forecasting using SVR produced best results, moreover its showed that the feature selection with FPSO was better than the features selection with original Particle Swarm Optimization.

An experimental study of fitness function and time series forecasting using artificial neural networks

Artificial Neural Networks (ANN) have been widely used in order to solve the time series forecasting problem and one of its most promising approach is the combination with other intelligent techniques, such as genetic algorithms, evolutionary strategies, etc. The choice of a good fitness function still an open question for the practitioners who use these techniques to solve the forecasting problem. The effectiveness and efficiency of the fitness functions proposed in the literature have not been compared among them. Based on five well-known (in the literature) measures of statistical errors and using three non linear time series, this paper empirically compares distinct fitness functions (instead of conventional MSE based ones). They are analysed using two hybrid methods for tuning ANN structure and parameters (a simplified but still realistic method called GRASPES and a modified genetic Algorithm).