A new class of wavelet networks for nonlinear system identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions

European exchange trading funds trading with locally weighted support vector regression

In this paper, two different Locally Weighted Support Vector Regression (wSVR) algorithms are generated and applied to the task of forecasting and trading five European Exchange Traded Funds. The trading application covers the recent European Monetary Union debt crisis. The performance of the proposed models is benchmarked against traditional Support Vector Regression (SVR) models. The Radial Basis Function, the Wavelet and the Mahalanobis kernel are explored and tested as SVR kernels. Finally, a novel statistical SVR input selection procedure is introduced based on a principal component analysis and the Hansen, Lunde, and Nason (2011) model confidence test. The results demonstrate the superiority of the wSVR models over the traditional SVRs and of the v-SVR over the ε-SVR algorithms. We note that the performance of all models varies and considerably deteriorates in the peak of the debt crisis. In terms of the kernels, our results do not confirm the belief that the Radial Basis Function is the optimum choice for financial series

Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network

In this study, 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 another 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 {\it stochastic} hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute 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 ($\sigma_{N}$) from 0.01 to 0.1.Comment: 11 pages, 8 figure

Lazy learning in radial basis neural networks: A way of achieving more accurate models

Radial Basis Neural Networks have been successfully used in a large number of applications having in its rapid convergence time one of its most important advantages. However, the level of generalization is usually poor and very dependent on the quality of the training data because some of the training patterns can be redundant or irrelevant. In this paper, we present a learning method that automatically selects the training patterns more appropriate to the new sample to be approximated. This training method follows a lazy learning strategy, in the sense that it builds approximations centered around the novel sample. The proposed method has been applied to three different domains an artificial regression problem and two time series prediction problems. Results have been compared to standard training method using the complete training data set and the new method shows better generalization abilities.Publicad

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework

Analysis of Daily Streamflow Complexity by Kolmogorov Measures and Lyapunov Exponent

Analysis of daily streamflow variability in space and time is important for water resources planning, development, and management. The natural variability of streamflow is being complicated by anthropogenic influences and climate change, which may introduce additional complexity into the phenomenological records. To address this question for daily discharge data recorded during the period 1989-2016 at twelve gauging stations on Brazos River in Texas (USA), we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures to assess complexity, and Lyapunov time (LT) to assess predictability. We find that all daily discharge series exhibit long memory with an increasing downflow tendency, while the randomness of the series at individual sites cannot be definitively concluded. All Kolmogorov complexity measures have relatively small values with the exception of the USGS (United States Geological Survey) 08088610 station at Graford, Texas, which exhibits the highest values of these complexity measures. This finding may be attributed to the elevated effect of human activities at Graford, and proportionally lesser effect at other stations. In addition, complexity tends to decrease downflow, meaning that larger catchments are generally less influenced by anthropogenic activity. The correction on randomness of Lyapunov time (quantifying predictability) is found to be inversely proportional to the Kolmogorov complexity, which strengthens our conclusion regarding the effect of anthropogenic activities, considering that KC and LT are distinct measures, based on rather different techniques