Abstract
An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ N) from 0.01 to 0.1.
Highlights
The prediction of time series has played an important role in many science fields of practical application as engineering, biology, physics, meteorology, and so forth
A hybrid algorithm based on artificial neural network and particle swarm optimization (ANN+PSO) is used in the short-term x(t + 6) prediction of Mackey-Glass chaotic time series
artificial neural networks (ANN)+PSO for the Mackey-Glass chaotic time series. This corresponds to the case with a white noise of σN = 0.1
Summary
The prediction of time series has played an important role in many science fields of practical application as engineering, biology, physics, meteorology, and so forth. Due to their dynamical properties, the analysis and prediction of chaotic time series have been of interest for the science community. Many methods have been used in the chaotic time series analysis [4]. In the last decades, different types of artificial neural networks (ANN) have been widely used for forecasting of chaotic time series, for example, backpropagation algorithm [5], radial basic function [6], and recurrent network [7]. The analysis of real-life time series requires taking into account the error propagation of input uncertainties. In the modeling of chaotic time series, the impact of noise can be treated as errors-invariable problem where the noise is propagated into the prediction model
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