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M4 forecasting competition provided some useful information to forecasting literature. The provided information is based on calculated error metrics for ranking methods in the competition. The organizers of the competition calculated arithmetic mean as a descriptive statistic for evaluating the performance of all competitors. In this paper, the effect of different descriptive statistics for ranking of methods is investigated. It is found that the distribution of error metrics for competitor forecasting methods is not symmetric. Thus, the arithmetic mean descriptive statistic is not a good metric to determine the centre of non-symmetric distributions and it will not well present centre of the distribution. In this study, it is showed that the median will well present centre of distribution for error metrics of competitor forecasting methods. When the median is used as a descriptive statistic for ranking methods, the ranks of methods is different form ranks which are calculated according to the arithmetic mean descriptive statistics. Moreover, the direction accuracy metric is calculated for the best ten methods in the competition. So, the forecasting methods are ranked according to direction accuracy and it is showed that the ranks are different from the competition results.

The Turkish Journal of Forecasting (TJF) is anopen access international journal and it is published semi-annually. The aim ofthe TJF is to procure a platform to integrate the research subjects and fields,and to bridge over the between theory and practice dealing with any aspect offorecasting. The first issue is regular, the second issue is a special issuefor International Web Conference on Forecasting. There is no any subscriptionfee, submission fee or publishing fee. All submitted papers will go through theblind review process, and the Associate Editors assign the manuscripts to atleast two reviewers, depending on article type. First two issues of the TJF arepublished in 2017 and a comprehensive summary ofthe issues are given in this editorial.

The aim of this study was to assess the frequency of the BMC phenomenon in a Turkish patient population. Cone beam computed tomography (CBCT) images of 2634 consecutive patients were retrospectively reviewed. The Chi-squared test was used to determine potential differences in the distribution of BMCs when stratified by sex and side. Among the 2634 patients, 42 (1.7%) patients were found to have BMC. Of these 42 patients, 22 were female (0.8%) and 20 were male (0.7%) with age ranging from 29 to 68 years (mean age 47.47). Among the 42 patients, 39 (92.8%) of the BMCs were unilateral and three (7.1%) were bilateral. Approximately 24 cases (53.3%) were on the right side, and 21 cases (46.6%) were on the left side. All of the BMCs showed a mediolateral orientation. The mean depth of the BMC was 2.55 mm in males and 2.68 mm in females. 2 patients have symptoms whereas the other patients were atraumatic and asymptomatic. BMC is a rare condition that might be more prevalent in the Turkish population. Greater detailed information regarding BMC could be obtained by the widespread use of CBCT in epidemiological studies. El objetivo de este estudio fue evaluar la frecuencia del fenómeno CMB en una población de pacientes de Turquía. Se revisaron imágenes consecutivas de tomografía computarizada (CBCT) de 2.634 pacientes retrospectivamente. Se utilizó la prueba de Chi-cuadrado para determinar las posibles diferencias en la distribución de CMB estratificado por sexo y lado. Entre los 2.634 pacientes, se encontró que 42 (1,7%) pacientes tenían CMB. De estos 42 pacientes, 22 eran mujeres (0,8%) y 20 eran varones (0,7%), con edades entre 29 a 68 años (promedio edad 47,47). Entre los 42 pacientes, 39 (92,8%) del CMB fueron unilaterales y tres (7,1%) fueron bilaterales. Aproximadamente 24 casos (53,3%) estaban en el lado derecho, y 21 casos (46,6%) estaban en el lado izquierdo. Todas las CMB mostraron una orientación mediolateral. La profundidad media de la CMB era 2,55 mm en los hombres y 2,68 mm en las mujeres. Dos de los pacientes presentaron síntomas, mientras que en el resto de los pacientes no presentó trauma ni síntomas. CMB es una afección poco común que podría ser más frecuente en la población turca. Mayor información y detalle sobre CMB se podría obtener en estudios epidemiológicos con el uso generalizado de CBCT.

2nd World Conference on Business, Economics and Management (BEM) -- APR 25-28, 2013 -- Antalya, TURKEY WOS: 000335570200182 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. (C) 2014 The Authors. Published by Elsevier Ltd. Selection and peer review under responsibility of Organizing Committee of BEM 2013. SciencePark Res, Org & Counseling Ltd, Acad World Educ & Res Ctr, Hacettepe Univ, Eastern Mediterranean Univ, Near E Univ, Zirve Univ

Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.

WOS: 000374578800011, Multiplicative neuron model-based artificial neural networks are one of the artificial neural network types which have been proposed recently and have produced successful forecasting results. Sigmoid activation function was used in multiplicative neuron model-based artificial neural networks in the previous studies. Although artificial neural networks which involve the use of radial basis activation function produce more successful forecasting results, Gaussian activation function has not been used for multiplicative neuron model yet. In this study, rather than using a sigmoid activation function, Gaussian activation function was used in multiplicative neuron model artificial neural network. The weights of artificial neural network and parameters of activation functions were optimized by guaranteed convergence particle swarm optimization. Two major contributions of this study are as follows: the use of Gaussian activation function in multiplicative neuron model for the first time and the optimizing of central and propagation parameters of activation function with the weights of artificial neural network in a single optimization process. The superior forecasting performance of the proposed Gaussian activation function-based multiplicative neuron model artificial neural network was proved by applying it to real-life time series.

WOS: 000277726300038, Univariate fuzzy time series approaches which have been widely used in recent years can be divided into two classes, which are called first order and high order models. In the literature, it has been shown that high order fuzzy time series approaches improve the forecasting accuracy. One of the important parts of obtaining high accuracy forecasts in fuzzy time series is that the length of interval is very vital. As mentioned in the first-order models by Egrioglu, Aladag, Basaran, Uslu, and Yolcu (2009), the length of interval also plays very important role in high order models too. In this study, a new approach which uses an optimization technique with a single-variable constraint is proposed to determine an optimal interval length in high order fuzzy time series models. An optimization procedure is used in order to determine optimum length of interval for the best forecasting accuracy, we used optimization procedure. In the optimization process, we used a MATLAB function employing an algorithm based on golden section search and parabolic interpolation. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results. (C) 2009 Elsevier Ltd. All rights reserved.

WOS: 000274554900021, Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results. (C) 2009 Elsevier B.V. All rights reserved.

WOS: 000264528600011, In the literature, there have been many studies using fuzzy time series for the purpose of forecasting. The most studied model is the first order fuzzy time series model. In this model, an observation of fuzzy time series is obtained by using the previous observation. In other words, only the first tagged variable is used when constructing the first order fuzzy time series model. Therefore, this model can not be sufficient for some time series such as seasonal time series which is an important class in time series models. Besides, the time series encountered in real life have not only autoregressive (AR) structure but also moving average (MA) structure. The fuzzy time series models available in the literature are AR structured and are not appropriate for MA structured time series. In this paper, a hybrid approach is proposed in order to analyze seasonal fuzzy time series. The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper. The order of this model is determined by utilizing Box-Jenkins method. In order to show the efficiency of the proposed hybrid method, real time series are analyzed with this method. The results obtained from the proposed method are compared with the other methods. As a result, it is observed that more accurate results are obtained from the proposed hybrid method. (C) 2008 Elsevier Ltd. All rights reserved.

WOS: 000286099100002, In fuzzy time series analysis, the determination of the interval length is an important issue. In many researches recently done, the length of intervals has been intuitively determined. In order to efficiently determine the length of intervals, two approaches which are based on the average and the distribution have been proposed by Huarng [4]. In this paper, we propose a new method based on the use of a single variable constrained optimization to determine the length of interval. In order to determine optimum length of interval for the best forecasting accuracy, we used aMATLAB function which is employing an algorithm based on golden section search and parabolic interpolation. Mean square error is used as a measure of forecasting accuracy so the objective function value is mean square error value for forecasted observations. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.

WOS: 000263584100009, A given observation in time series does not only depend on preceding one but also previous ones in general. Therefore, high order fuzzy time series approach might obtain better forecasts than does first order fuzzy time series approach. Defining fuzzy relation in high order fuzzy time series approach are more complicated than that in first order fuzzy time series approach. A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced in this paper. The new proposed approach is applied to well-known enrollment data for the University of Alabama and obtained results are compared with other methods proposed in the literature. It is found that the proposed method produces better forecasts than the other methods. (c) 2008 Elsevier Ltd. All rights reserved.

13th World Conference on Soft Computing in Industrial Application -- 2008 -- ELECTR NETWORK, WOS: 000269657800026, When observations of time series are defined linguistically or do not follow the assumptions required for time series theory, the classical methods of time series analysis do not cope with fuzzy numbers and assumption violations. Therefore, forecasts are not reliable. [8], [9] gave a definition of fuzzy time series which have fuzzy observations and proposed a forecast method for it. In recent years, many researches about univariate fuzzy time series have been conducted. In [6], [5], [7], [4] and [10] bivariate fuzzy time series approaches have been proposed. In this study, a new method for high order bivariate fuzzy time series in which fuzzy relationships are determined by artificial neural networks (ANN) is proposed and the real data application of the proposed method is presented., World Federat Soft Comp, IEEE Ind Applicat Soc, IEEE UKRI Sect, Elsevier

WOS: 000262888100021, In the implementations of fuzzy time series forecasting, the identification of interval lengths has an important impact on the performance of the procedure. However, the interval length has been chosen arbitrarily in many papers. Huarng developed a new approach which is called ratio-based lengths of intervals in order to identify the length of intervals. In our paper, we propose a new approach which uses a single-variable constrained optimization to determine the ratio for the length of intervals. The proposed approach is applied to the two well-known time series, which are enrollment data at The University of Alabama and inventory demand data. The obtained results are compared to those of other methods. The proposed method produces more accurate predictions for the future values of used time series. (c) 2008 Elsevier B.V. All rights reserved.

WOS: 000266851000044, Fuzzy time series methods have been recently becoming very popular in forecasting. These methods can be categorized into two subclasses that are univariate and multivariate approaches. It is a known fact that real time series data can actually be affected by many factors. In this case, the using multivariate fuzzy time series forecasting model can be more reasonable in order to get more accurate forecasts. To obtain fuzzy forecasts when multivariate fuzzy time series approach is adopted, the most applied method is using tables of fuzzy relations. However, employing this method is a computationally though task. In this study, we introduce a new method that does not require using fuzzy logic relation tables in order to determine fuzzy relationships. Instead, a feed forward artificial neural network is employed to determine fuzzy relationships. The proposed method is applied to the time series data of the total number of annual car road accidents casualties in Belgium from 1974 to 2004 and a comparison is made between our proposed method and the methods proposed by Jilani and Burney [Jilani, T. A., & Burney, S. M. A. (2008). Multivariate stochastic fuzzy forecasting models. Expert Systems with Applications, 35, 691-700] and Lee et al. [Lee, L.-W., Wang, L.-H., Chen, S.-M., & Leu, Y.-H. (2006). Handling forecasting problems based on two factors high order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14, 468-477]. (C) 2009 Elsevier Ltd. All rights reserved.

Akdeniz, Esra/0000-0002-3549-5416; Bas, Eren/0000-0002-0263-8804; Egrioglu, Erol/0000-0003-4301-4149 WOS: 000432541000004 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.