Eren Bas

The training of multiplicative neuron model based artificial neural networks with differential evolution algorithm for forecasting

Abstract In recent years, artificial neural networks have been commonly used for time series forecasting by researchers from various fields. There are some types of artificial neural networks and feed forward artificial neural networks model is one of them. Although feed forward artificial neural networks gives successful forecasting results they have a basic problem. This problem is architecture selection problem. In order to eliminate this problem, Yadav et al. (2007) proposed multiplicative neuron model artificial neural network. In this study, differential evolution algorithm is proposed for the training of multiplicative neuron model for forecasting. The proposed method is applied to two well-known different real world time series data.

A modified genetic algorithm for forecasting fuzzy time series

Fuzzy time series approaches are used when observations of time series contain uncertainty. Moreover, these approaches do not require the assumptions needed for traditional time series approaches. Generally, fuzzy time series methods consist of three stages, namely, fuzzification, determination of fuzzy relations, and defuzzification. Artificial intelligence algorithms are frequently used in these stages with genetic algorithms being the most popular of these algorithms owing to their rich operators and good performance. However, the mutation operator of a GA may cause some negative results in the solution set. Thus, we propose a modified genetic algorithm to find optimal interval lengths and control the effects of the mutation operator. The results of applying our new approach to real datasets show superior forecasting performance when compared with those obtained by other techniques.

A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations

Fuzzy time series approaches, which do not require the strict assumptions of traditional time series approaches, generally consist of three stages. These are called as the fuzzification of crisp time series observations, the identification of fuzzy relationships and the defuzzification. All of these stages play a very important role on the forecasting performance of the model. Although there are many studies contributing to the stages of fuzzification and determining fuzzy relationships, the number of the studies about the defuzzification stage, which is very important at least as much as the others, is limited. None of them considered the number of recurrence of the fuzzy relationships in the stage of defuzzification. However it is very reasonable to take into account since fuzzy relations and their recurrence number are reflected the nature of the time series. Then the information obtained from the fuzzy relationships can be used in the defuzzification stage. In this study, we take into account the recurrence number of the fuzzy relations in the stage of defuzzification. Then this new approach has been applied to the real data sets which are often used in other studies in literature. The results are compared to the ones obtained from other techniques. Thus it is concluded that the results present superior forecasts performance.

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

Non-probabilistic forecasting methods are commonly used in various scientific fields. Fuzzy-time-series methods are well-known non-probabilistic and nonlinear forecasting methods. Although these methods can produce accurate forecasts, linear autoregressive models can produce forecasts that are more accurate than those produced by fuzzy-time-series methods for some real-world time series. It is well known that hybrid forecasting methods are useful techniques for forecasting time series and that they have the capabilities of their components. In this study, a new hybrid forecasting method is proposed. The components of the new hybrid method are a high-order fuzzy-time-series forecasting model and autoregressive model. The new hybrid forecasting method has a network structure and is called a fuzzy-time-series network (FTS-N). The fuzzy c-means method is used for the fuzzification of time series in FTS-N, which is trained by particle swarm optimization. Istanbul Stock Exchange daily data sets from 2009 to 2013 and the Taiwan Stock Exchange Capitalization Weighted Stock Index data sets from 1999 to 2004 were used to evaluate the performance of FTS-N. The applications reveal that FTS-N produces more accurate forecasts for the 11 real-world time-series data sets.

Fuzzy lagged variable selection in fuzzy time series with genetic algorithms

Fuzzy time series forecasting models can be divided into two subclasses which are first order and high order. In high order models, all lagged variables exist in the model according to the model order. Thus, some of these can exist in the model although these lagged variables are not significant in explaining fuzzy relationships. If such lagged variables can be removed from the model, fuzzy relationships will be defined better and it will cause more accurate forecasting results. In this study, a new fuzzy time series forecasting model has been proposed by defining a partial high order fuzzy time series forecasting model in which the selection of fuzzy lagged variables is done by using genetic algorithms. The proposed method is applied to some real life time series and obtained results are compared with those obtained from other methods available in the literature. It is shown that the proposed method has high forecasting accuracy.

Robust learning algorithm for multiplicative neuron model artificial neural networks

A new robust learning algorithm was proposed for multiplicative neuron model (MNM).The proposed method gives successful results even when data sets have outliers.There is no a robust learning algorithm in the literature for MNM.The performance of proposed method was supported with real time series data.A simulation study was performed to show the performance of the proposed method. The two most commonly used types of artificial neural networks (ANNs) are the multilayer feed-forward and multiplicative neuron model ANNs. In the literature, although there is a robust learning algorithm for the former, there is no such algorithm for the latter. Because of its multiplicative structure, the performance of multiplicative neuron model ANNs is affected negatively when the dataset has outliers. On this issue, a robust learning algorithm for the multiplicative neuron model ANNs is proposed that uses Hubers loss function as fitness function. The training of the multiplicative neuron model is performed using particle swarm optimization. One principle advantage of this algorithm is that the parameter of the scale estimator, which is an important factor affecting the value of Hubers loss function, is also estimated with the proposed algorithm. To evaluate the performance of the proposed method, it is applied to two well-known real world time series datasets, and also a simulation study is performed. The algorithm has superior performance both when it is applied to real world time series datasets and the simulation study when compared with other ANNs reported in the literature. Another of its advantages is that, for datasets with outliers, the results are very close to the results obtained from the original datasets. In other words, we demonstrate that the algorithm is unaffected by outliers and has a robust structure.

Recurrent Multiplicative Neuron Model Artificial Neural Network for Non-linear Time Series Forecasting

Artificial neural networks (ANN) have been widely used in recent years to model non-linear time series since ANN approach is a responsive method and does not require some assumptions such as normality or linearity. An important problem with using ANN for time series forecasting is to determine the number of neurons in hidden layer. There have been some approaches in the literature to deal with the problem of determining the number of neurons in hidden layer. A new ANN model was suggested which is called multiplicative neuron model (MNM) in the literature. MNM has only one neuron in hidden layer. Therefore, the problem of determining the number of neurons in hidden layer is automatically solved when MNM is employed. Also, MNM can produce accurate forecasts for non-linear time series. ANN models utilized for non-linear time series have generally autoregressive structures since lagged variables of time series are generally inputs of these models. On the other hand, it is a well-known fact that better forecasts for real life time series can be obtained from models whose inputs are lagged variables of error. In this study, a new recurrent multiplicative neuron neural network model is firstly proposed. In the proposed method, lagged variables of error are included in the model. Also, the problem of determining the number of neurons in hidden layer is avoided when the proposed method is used. To train the proposed neural network model, particle swarm optimization algorithm was used. To evaluate the performance of the proposed model, it was applied to a real life time series. Then, results produced by the proposed method were compared to those obtained from other methods. It was observed that the proposed method has superior performance to existing methods.

An ARMA Type Pi-Sigma Artificial Neural Network for Nonlinear Time Series Forecasting

Abstract Real-life time series have complex and non-linear structures. Artificial Neural Networks have been frequently used in the literature to analyze non-linear time series. High order artificial neural networks, in view of other artificial neural network types, are more adaptable to the data because of their expandable model order. In this paper, a new recurrent architecture for Pi-Sigma artificial neural networks is proposed. A learning algorithm based on particle swarm optimization is also used as a tool for the training of the proposed neural network. The proposed new high order artificial neural network is applied to three real life time series data and also a simulation study is performed for Istanbul Stock Exchange data set.

Single Multiplicative Neuron Model Artificial Neural Network with Autoregressive Coefficient for Time Series Modelling

Single multiplicative neuron model and multilayer perceptron have been commonly used for time series prediction problem. Having a simple structure and features of easily applicable differentiates the single multiplicative neuron model from the multilayer perception. While, multilayer perceptron just as many other artificial neural networks are data-based methods, single multiplicative neuron model has a model structure due to it is composed of a single neuron. Multilayer perceptron can highly compliance with data by changing its architecture, though single multiplicative neuron model, in this respect, is insufficient. In this study, to overcome this problem of single multiplicative neuron model, a new model that its weights and biases are obtained by way of autoregressive equations is proposed. Since the time indexes are considered to determine weights and biases from the autoregressive models, the proposed neural network can be evaluated as a data-based model. To show the performance and capability of the proposed method, various implementations have been executed over some well-known data sets. And the obtained results demonstrate that data-based proposed method has outstanding forecasting performance.

Median-Pi artificial neural network for forecasting

Datasets with outliers can be predicted with robust learning methods or robust artificial neural networks. In robust artificial neural networks, the architectures become robust by using robust statistics as aggregation functions. Median neural network and trimmed mean neural network are two robust artificial neural networks used in the literature. In these robust artificial neural networks, median and trimmed mean statistics are used as aggregation functions. In this study, Median-Pi artificial neural network is proposed as a new robust neural network for the purpose of forecasting. In Median-Pi artificial neural network, median and multiplicative functions are used as aggregation functions. Because of using median, the proposed network can produce good results for data with outliers. The Median-Pi artificial neural network is trained by particle swarm optimization. The performance of the neural network is investigated by using datasets from the International Time Series Forecast Competition 2016 (CIF-2016). The performance of the proposed method in case of outlier is compared to some other artificial neural networks. Median neural network, trimmed mean neural network, Pi-Sigma neural network and the proposed robust network are applied to time series with outlier, and the obtained results are compared. According to application results, the proposed Median-Pi artificial neural network can produce better forecast results than the other network types.