Fuzzy-time-series network used to forecast linear and nonlinear time series

Day ahead price forecasting of electricity markets by a mixed data model and hybrid forecast method

In this study, a new hybrid forecasting method is proposed. The proposed method is called autoregressive adaptive network fuzzy inference system (AR---ANFIS). AR---ANFIS can be shown in a network structure. The architecture of the network has two parts. The first part is an ANFIS structure and the second part is a linear AR model structure. In the literature, AR models and ANFIS are widely used in time series forecasting. Linear AR models are used according to model-based strategy. A nonlinear model is employed by using ANFIS. Moreover, ANFIS is a kind of data-based modeling system like artificial neural network. In this study, a linear and nonlinear forecasting model is proposed by creating a hybrid method of AR and ANFIS. The new method has advantages of data-based and model-based approaches. AR---ANFIS is trained by using particle swarm optimization, and fuzzification is done by using fuzzy C-Means method. AR---ANFIS method is examined on some real-life time series data, and it is compared with the other time series forecasting methods. As a consequence of applications, it is shown that the proposed method can produce accurate forecasts.

Even in sustained vowels, the durations of successive glottal cycles are not identical. They fluctuate quasi-randomly around an average. This phenomenon is known as jitter. Correlation analysis has shown that perturbations of neighboring glottal cycles are interdependent, i.e. they are not purely random. The non-random component of jitter can be modeled by means of a linear autoregressive time series model which absorbs correlations between fluctuations of adjacent cycles and leaves a purely random component. The problem is that nonlinear relations may be missed by correlation analysis or linear autoregressive modeling. Nonlinear relations could be the signature of chaotic vibratory patterns which some authors expect for some pathological conditions of the vocal folds. We therefore decided to search inside whitened jitter time series (i.e. time series from which any linear correlations had been removed) for nonlinear or other anomalous dependencies between neighboring cycles. The results showed the following. Of the 265 time series, 231 appeared to have been correctly represented by linear autoregressive models. For 29 series out of the 34 remaining, deviations from pure randomness could be traced to isolated anomalous glottal cycles which statistical time series models had not taken into account. Finally, five signals, produced by three speakers, were detected which displayed relations between neighboring cycles which could not be traced either to linear correlations or to isolated glitches.

Short-term load forecasting of power systems by combination of wavelet transform and neuro-evolutionary algorithm

Artificial Neural networks (ANN) are powerful and effective tools in time-series applications. The first aim of this paper is to diagnose better and more efficient ANN models (Back Propagation, Radial Basis Function Neural networks (RBF), and Recurrent neural networks) in solving the linear and nonlinear time-series behavior. The second aim is dealing with finding accurate estimators as the convergence sometimes is stack in the local minima. It is one of the problems that can bias the test of the robustness of the ANN in time series forecasting. To determine the best or the optimal ANN models, forecast Skill (SS) employed to measure the efficiency of the performance of ANN models. The mean square error and the absolute mean square error were also used to measure the accuracy of the estimation for methods used. The important result obtained in this paper is that the optimal neural network was the Backpropagation (BP) and Recurrent neural networks (RNN) to solve time series, whether linear, semilinear, or non-linear. Besides, the result proved that the inefficiency and inaccuracy (failure) of RBF in solving nonlinear time series. However, RBF shows good efficiency in the case of linear or semi-linear time series only. It overcomes the problem of local minimum. The results showed improvements in the modern methods for time series forecasting.

Short-term load forecasting method based on fuzzy time series, seasonality and long memory process

In this paper, a new feature selection and forecast engine is presented for day ahead prediction of electricity prices, which are so valuable for both producers and consumers in the new competitive electric power markets. In a competitive electricity market, forecast of energy prices is a key information for the market participants. However, price signal usually has a complex behavior due to its nonlinearity, non-stationary, and time variance. Also, an appropriate feature selection is crucial for accurate forecasting. In this paper, a two-step approach that identifies a set of candidate features based on the data characteristics proposed and then selects a subset of them using correlation and instance-based feature selection methods, applied in a systematic way. Then, a combination of wavelet transform (WT) and a hybrid forecast method is presented based on neural network (NN) and an optimization algorithms. The proposed method is examined on PJM electricity market and compared with some of the most recent price forecast methods. These comparisons illustrate effectiveness of the proposed strategy.

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.

Time series forecasting research area generally aims at improving prediction accuracy. Discrete wavelet transform (DWT) has been applied to time series for decomposing it into approximation and detail. Nevertheless, typically, the property of the approximation and the detail are presumed as either linear or nonlinear. Actually, the purpose of the DWT is not decomposing the original time series into linear and nonlinear time series. Hence, this paper develops a new hybrid model of autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and the DWT without prior assumption on linear and nonlinear property of the approximation and the detail. The different Khashei and Bijari’s hybrid models involving the ARIMA and the ANN are built for the approximation and the detail in order to extract their both linear and nonlinear components and fit the relationship between the components as the function instead of additive relationship. Finally, the forecasted approximation and detail are combined to obtain final forecasting. The prediction capability of the proposed model is examined with two well-known time series: the sunspot and the Canadian lynx time series. The results show that the proposed model has the best performance in all two data sets and all three measures (i.e. MSE, MAE and MAPE).

Non-Linear Forecasting Methods: Some Applications to the Analysis of Financial Series

Seasonality is a distinctive characteristic which is often observed in many practical time series. Artificial Neural Networks (ANNs) are a class of promising models for efficiently recognizing and forecasting seasonal patterns. In this paper, the Particle Swarm Optimization (PSO) approach is used to enhance the forecasting strengths of feedforward ANN (FANN) as well as Elman ANN (EANN) models for seasonal data. Three widely popular versions of the basic PSO algorithm, viz. Trelea-I, Trelea-II and Clerc-Type1 are considered here. The empirical analysis is conducted on three real-world seasonal time series. Results clearly show that each version of the PSO algorithm achieves notably better forecasting accuracies than the standard Backpropagation (BP) training method for both FANN and EANN models. The neural network forecasting results are also compared with those from the three traditional statistical models, viz. Seasonal Autoregressive Integrated Moving Average (SARIMA), Holt-Winters (HW) and Support Vector Machine (SVM). The comparison demonstrates that both PSO and BP based neural networks outperform SARIMA, HW and SVM models for all three time series datasets. The forecasting performances of ANNs are further improved through combining the outputs from the three PSO based models.

This study compares the efficiency of a non-linear model called artificial neural network with linear autoregressive and random walk models in the one-step-ahead prediction of daily Indian rupee/US dollar exchange rate. We find that neural network and linear autoregressive models outperform random walk model in in-sample and out-of-sample forecasts. The in-sample forecasting of neural network is found to be better than that of linear autoregressive model. As far as out-of-sample forecasting is concerned, the results are mixed and we do not find a "winner" model between neural network and linear autoregressive model. However, neural network is able to improve upon the linear autoregressive model in terms of sign predictions. In addition to this, we also find that the number of input nodes has greater impact on neural network's performance than the number of hidden nodes.

A hybrid evolutionary decomposition system for time series forecasting

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Transportation is one of the major carbon sources in China. Container throughput is one of the main influencing factors of ports’ carbon emission budget, and accurate prediction of container throughput is of great significance to the study of carbon emissions. Time series methods are key techniques and frequently used for container throughput. However, the existing time series methods treat container throughput data as discrete points and ignore the functional characteristics of the data. There has recently been interest in developing new statistical methods to predict time series by taking into account a continuous set of past values as predictors. In addition, to eliminate the linear constraint in the functional time series prediction approach, we propose a functional version of a nonparametric model that allows using a continuous path in the past to predict future values of the process, including functional nonparametric regression and functional conditional quantile and functional conditional mode models, to forecast the container throughput of Shanghai Port. For the purpose better forecasting, an experiment was conducted to compare our functional data analysis approaches with other forecasting methods. The results indicated that nonparametric functional forecasting methods exhibit more significant performance than other classical models, including the functional linear regression model, nonparametric regression model, and autoregressive integrated moving-average model. At the same time, we also compared the prediction accuracy of the three nonparametric functional methods.