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The increase of the world population, especially in the global competition, together with the increasing use of fossil fuel resources to meet energy needs, leads to more greenhouse gases (more than one CO2, methane etc.) emissions and the global climate crisis. In this process, changes in meteorological events such as temperature, precipitation, and wind, attract attention moreover but when considered as a whole, we know that these negative changes in the ecosystem negatively affect many living groups. Sea Surface Temperature (SST) as measured meteorologically is the most important environmental parameter where these changes are monitored and observed. It draws attention to the fact that changes in SST are not limited to living organisms as habitats, but also catalyze many chain reactions, especially socio-economic impacts. Therefore, much of the work is devoted to forecasting studies to adapt to changing habitats and take the necessary precautions against potential risks. Feed-forward artificial neural networks have been commonly used to address these emerging needs. Artificial neural networks, which are a simple imitation of the human neurological system, have been used as an artificial intelligence method in forecasting problems due to their superior performance and not having the limitations of classical time series. In this study, the forecasting of the time series of monthly mean SST temperature obtained from Rize station between the years 2010 and 2020 is performed by using feed-forward artificial neural networks, and the forecasting performance of the corresponding time series is compared with many forecasting methods with different characteristics. The comparison of the methods used the mean square error and mean absolute percentage error criteria, which are commonly used in the forecasting literature. The analysis results showed that the analysis results obtained with the feed-forward artificial neural networks have the best prediction performance. As a result, it can be stated that the sea surface temperature can be forecasted with a very high accuracy using the feed-forward artificial neural networks.

Deep artificial neural networks have become a good alternative to classical forecasting methods in solving forecasting problems. Popular deep neural networks classically use additive aggregation functions in their cell structures. It is available in the literature that the use of multiplicative aggregation functions in shallow artificial neural networks produces successful results for the forecasting problem. A type of high-order shallow artificial neural network that uses multiplicative aggregation functions is the dendritic neuron model artificial neural network, which has successful forecasting performance. The first contribution of this work is the transformation of the dendritic neuron model, which works with a single output in the literature, into a multi-output architecture. The second contribution is to propose a new dendritic cell based on the multi-output dendritic neuron model for use in deep artificial neural networks. The other most important contribution of the study is to propose a new deep artificial neural network, a deep dendritic artificial neural network, based on the dendritic cell. The training of the deep dendritic artificial neural network is carried out with the differential evolution algorithm. The forecasting performance of the deep dendritic artificial neural network is compared with basic classical forecasting methods and some recent shallow and deep artificial neural networks over stock market time series. As a result, it has been observed that deep dendritic artificial neural network produces very successful forecasting results for the forecasting problem.

The model adequacy and input significance tests have not been proposed as features for the specification of a single multiplicative neuron model artificial neural networks in the literature. Moreover, there is no systematic approach based on hypothesis tests for using single multiplicative neuron model artificial neural networks for forecasting purposes like classical time series forecasting methods. In this study, new methods are proposed to solve these problems. The performance of the proposed test procedures is investigated in a simulation study. According to simulation results, the proposed tests have very good performance. Moreover, the test procedures are illustrated by using two real-world examples. The second contribution of the paper is that an automatic forecasting method is proposed based on input significance and model adequacy tests and the particle swarm optimization-based learning algorithm. The proposed automatic forecasting method is applied to M4 competition hourly data sets, and it is the best pure machine learning method among others in the competition. The proposed automatic forecasting method is more accurate than all benchmarks, such as MLP, RNN, and ETS, which were proposed by the competition organizers.

Artificial neural network models have been frequently used in time series forecasting problems as an alternative to many classical forecasting models. Although multi-layer perceptron neural networks are one of the most frequently used artificial neural networks in the literature, high-order neural networks using high-order combinations of inputs have superior performance compared to multi-layer perceptron artificial neural networks in recent years. Although there are many highorder artificial neural networks with different properties in the literature, one of the most important problems of these highorder artificial neural networks is to determine the optimization method to be used in the training of the network structure. Sigma-Pi artificial neural networks, one of the high-order artificial neural networks, have been used frequently in many problems in recent years. Like many artificial neural networks, the training of the Sigma-Pi neural network is one of the important factors affecting the performance of the network. In this study, the grey wolf optimization algorithm is used for the first time in the literature in the training of Sigma-Pi artificial neural networks. Thus, a training process that does not require complex derivative calculations in derivative-based algorithms is performed. In the evaluation of the performance of the proposed method, the closing prices of the FTSE and S&P 500 are analyzed for different years. According to the analysis results, the proposed method has a 60% success rate for both FTSE and S&P 500 time series. For the comparison of all methods, the mean rank calculation is made for each method. The proposed method took first place in this ranking and is determined as the best method among all methods.

Picture fuzzy time series has been defined recently and a high order single variable forecasting method was proposed in the literature. Picture fuzzy time series definition is based on picture fuzzy sets which are the extended version of the fuzzy sets. So, more information is added for the modelling procedure with the use of picture fuzzy sets instead of classical fuzzy sets. In this study, high order multivariate picture fuzzy time series forecasting model is firstly defined and a forecasting algorithm based on this model is introduced. The proposed method uses picture fuzzy clustering and Pi-Sigma artificial neural networks as creating picture fuzzy time series and estimating of picture fuzzy forecasting model, respectively. The Pi-Sigma artificial neural network is trained by particle swarm optimization. The proposed method is applied to the TAIEX stock exchange data sets using Dow Jones and NASDAQ stock exchange data sets and Turkish lira exchange rates data sets using the dollar, euro and pound data sets as factor variables. The proposed method produces the best results among established benchmarks.

Deep artificial neural networks have been popular for time series forecasting literature in recent years. The recurrent neural networks present more suitable architectures for forecasting problems than other deep neural network types. The simplest deep recurrent neural network type is simple recurrent neural networks according to the number of employed parameters. These neural networks can be preferred to solve forecasting problems because of their simple structure if they are trained well. Unfortunately, the training of simple recurrent neural networks is problematic because of exploding or vanishing gradient problems. The contribution of this study is proposing a new training algorithm based on particle swarm optimization. The algorithm does not use gradients so it has not vanished or exploding gradient problem. The performance of the new training algorithm is compared with long short-term memory trained by the Adam algorithm and Pi-Sigma artificial neural network. In the applications, ten-time series are used to compare the performance of the methods. The ten-time series is consisting of daily observations of the Dow-Jones and Nikkei stock exchange opening prices between the years 2014 and 2018. At the end of the analysis processes, the proposed method produces more accurate forecast results than established benchmarks.

Looking at the artificial neural networks’ literature, most of the studies started with feedforward artificial neural networks and the training of many feedforward artificial neural networks models are performed with derivative-based algorithms such as levenberg–marquardt and back-propagation learning algorithms in the first studies. In recent years, although many new heuristic algorithms have been proposed for different aims these heuristic algorithms are also frequently used in the training process of many different artificial neural network models. Pi-sigma artificial neural networks have different importance than many artificial neural network models with its higher-order network structure and superior forecasting performance. In this study, the training of Pi-Sigma artificial neural networks is performed by differential evolution algorithm uses DE/rand/1 mutation strategy. The performance of the proposed method is evaluated by two data sets and seen that the proposed method has a very effective performance compared with many artificial neural network models.

The recurrent fuzzy time series function method can be obtained in two ways. First is using a similar model to the autoregressive moving average to obtain fuzzy functions and the second one is using recurrent connections in the combining equation. The recurrent structure provides less number of inputs and more accurate forecasts. The contribution of the paper is proposing a recurrent fuzzy time series function method and its bootstrapped version. The recurrent models are used to obtain fuzzy functions in the proposed method. The classical bootstrap method is applied and bootstrap samples are generated from learning samples. The bootstrap method provides lower forecast error variance for the proposed method. The performance of new methods is compared with some fuzzy function methods and classical approaches. First, Turkey electrical consumption data time series are analyzed. Second, the Australian beer consumption time series are analyzed. As a result of applications, new methods have good forecasting performance if compare to established benchmarks.

Background: Intuitionistic fuzzy time series forecasting methods have been started to solve the forecasting problems in the literature. Intuitionistic fuzzy time series methods use both membership and non-membership values as auxiliary variables in their models. Because intuitionistic fuzzy sets take into consideration the hesitation margin and so the intuitionistic fuzzy time series models use more information than fuzzy time series models. The background of this study is about intuitionistic fuzzy time series forecasting methods. Objective: The study aims to propose a novel intuitionistic fuzzy time series method. It is expected that the proposed method will produce better forecasts than some selected benchmarks. Method: The proposed method uses bootstrapped combined Pi-Sigma artificial neural network and intuitionistic fuzzy c-means. The combined Pi-Sigma artificial neural network is proposed to model the intuitionistic fuzzy relations. Results and Conclusion: The proposed method is applied to different sets of SP&500 stock exchange time series. The proposed method can provide more accurate forecasts than established benchmarks for the SP&500 stock exchange time series. The most important contribution of the proposed method is that it creates statistical inference: probabilistic forecasting, confidence intervals and the empirical distribution of the forecasts. Moreover, the proposed method is better than the selected benchmarks for the SP&500 data set.

WOS: 000466207000001 Time series can contain both linear and nonlinear components, and linear and nonlinear artificial neural networks (L&NL-ANNs) have been proposed to forecast them. Although L&NL-ANNs can produce well forecasting results, these neural networks have a handicap in point of view statistical science like other neural networks. The forecasts obtained from L&NL-ANNs may change depending on the time series samples, but this variation is neglected in the literature. The objective of this study has overcome this handicap and producing a method which can give point forecasts, confidence intervals and some weights significance hypothesis tests besides the proposed method performs linearity and nonlinearity hypothesis tests. The proposed method is compared with other conventional methods using a Monte Carlo simulation study and real-world time series data which are Nikkei 225, Dow Jones and Istanbul Stock Exchange time series datasets as well as Australian beer consumption time series. The performance of the proposed method is evaluated using the application and simulation results and found to perform well overall with respect to other methods. It is shown that bootstrapped L&NL-ANN produced the smallest mean and variance of forecast errors for results obtained from different random initial parameters.