Advances in Time Series Forecasting

In the literature, many models based on fuzzy systems have been utilized to solve various real world problems from different application areas. One of this areas is time series forecasting. Successful forecasting results have been obtained from fuzzy time series forecasting models in many studies. To determine the best fuzzy time series model among possible forecasting models is a vital decision. In order to evaluate fuzzy time series forecasting models, conventional performance measures such as root mean square error or mean absolute percentage error have been widely utilized in the literature. However, the nature of fuzzy logic is not taking into consideration when such conventional criteria are employed since these criteria are computed over crisp values. When fuzzy time series forecasting models are evaluated, using criteria which work based on fuzzy logic characteristics is wiser. Therefore, Aladag and Turksen [2] suggested a new performance measure which is calculated based on membership values to evaluate fuzzy systems. It is called as membership value based performance measure. In this study, a novel distance measure is firstly defined and a new membership value based performance measure based on this new distance measure is proposed. The proposed criterion is also applied to real world time series in order to show the applicability of the suggested measure.

Non-probabilistic forecasting methods are one of the most popular forecasting methods in recent years. Fuzzy time series methods are non-probabilistic and non-linear methods. Although these methods have superior forecasting performance, linear autoregressive models have better forecasting performance than fuzzy time series methods for some real-life time series. In this paper, a new hybrid forecasting method that contains stochastic approach based on an autoregressive model and fuzzy time series forecasting model was proposed in a network structure. Fuzzy c means method is used in fuzzification stage of the proposed method and also the proposed method is trained by using particle swarm optimization. The proposed method is applied to a well-known real-life time series data and it is proved that the proposed method has best forecasting performance when compared with some other studies suggested in the literature.

This paper presents an efficient and simplified type-1 and interval type-2 non singleton fuzzy logic systems (NSFLSs) in order to obviate time series forecasting problems. These methods have applied non singleton fuzzification by Sharp Gaussian membership function, logical inference with the First-Infer-Then-Aggregate (FITA) approach and parametric defuzzification. Rules are generated based on high order fuzzy time series. In interval type-2 FLS, which can better handle uncertainties, type-2 sets are generated, using fuzzy normal forms by applying Yager Parametric classes of operators. Moreover, in these systems, some elements such as membership functions, operators and length of intervals affect the forecasting results. In addition, a method for tuning parameters of fuzzy logic systems with genetic algorithm is presented. Finally, the proposed methods are applied to predict the temperature and the Taiwan Stock Exchange (TAIEX). The results show the higher degree of accuracy of the model compared to the previous methods.

Artificial neural networks have been commonly used for time series forecasting problem in the last years. When they are compared with classical time series methods, artificial neural networks have some advantages. Artificial neural networks do not need any assumption such as normality and linearity. In recent years, different types of artificial neural networks have been proposed for time series forecasting. In these networks, the inputs are lagged variables or other time series. It is well known that some time series have deterministic trend and this kind of time series should be modeled by using different functions of time (t) as inputs. In the modeling such type time series, using only lagged variables will lead to insufficient results. In this study, a new neural network model that has different functions of time as inputs is proposed for solving this problem. The proposed method is compared with other methods in the literature according to forecast performance. It is obtained that the new model outperforms other methods.

In the literature, two basic approaches are mentioned for time series forecasting. These are probabilistic and non-probabilistic approaches. This study is focused on fuzzy time series method one of the non-probabilistic approaches. Fuzzy time series analysis methods are the effective methods which are more favourable than traditional methods. The basic stages as fuzzification, identification of fuzzy relations and defuzzification which constitute the fuzzy time series analyses has been affectively used to get a better prediction performance. All of these three stages that are considered separately in analysis process lead to different errors. This situation, therefore, may cause a rise in model error. In order to eliminate this problem in this study all steps can be evaluated in one process synchronously. In the proposed approach, the method similar to fuzzy C-means, multiplicative artificial neural networks and genetic algorithm are used simultaneously in fuzzification, identification of fuzzy relation and determination of all parameters, respectively. And also different fuzzy time series are analysed. All obtained results are discussed to be able to consider the proposed method in terms of forecasting performance.

Stock exchanges forecasting is a popular research topic that is attracting more and more attention from researchers and practitioners. Since it is a well-known fact that stock exchanges time series include uncertainty, using conventional time series methods can lead to misleading results. Therefore, a proper approach should be employed for analysis according to the nature of the data. In the literature, fuzzy time series models have been successfully used to forecast real world time series which include vagueness. In order to handle uncertainty in stock exchanges, fuzzy time series forecasting approach proposed by Tsaur [17] is utilized in this study. Fuzzy time series forecasting model suggested by Tsaur [17] uses Markov chain transition matrix for fuzzy inference. In the implementation, the fuzzy time series forecasting model is applied to index 100 in stocks and bonds exchange market of İstanbul in order to show the performance of the model. It is seen that the forecasting model gives accurate forecasts for the data.

In many disciplines, including uncertainty of data obtained from time series problems generates the needs to use fuzzy time series methods which do not need to check some strict assumptions of conventional time series methods. Although, there are many other well-known prediction methods in the fuzzy time series literature, most of them comprise of univariate methods and these methods may fail to satisfy to analysis of the data which contain multivariate relationships. In this study, the new multivariate fuzzy time series approach is proposed. The proposed approach uses fuzzy C-means method to determine the membership values in the fuzzification stage, and also this new multivariate approach makes use of single multiplicative neuron model artificial neural network for the identification of the multivariate fuzzy relations. In the identification of fuzzy relations stage, membership values are used to avoid the information loss. The proposed methods’ performance has been assessed by applying it to different data sets.

After being proposed by Professor Lotfi A. Zadeh in 1965, fuzzy set theory has been used in many areas by researchers. Although fuzzy set theory has been used in many areas in the literature, implementation of fuzzy theories and techniques remains a difficult task, and it causes problems. One of these problems is to generate fuzzy ifthen rules. These rules can be constituted by an inference of knowledge of experts, but human knowledge is generally incomplete. With the above problems in hand, in place of fuzzy rule base structures, fuzzy functions approach was proposed by Turksen in 2008. In literature, fuzzy inference systems have been used for forecasting problems. Classical fuzzy inference systems are based on the rules. As mentioned before, fuzzy functions are not based on the rules, and this is an advantage for them. Fuzzy functions approach was carried out to obtain forecasts by using simultaneous variables of other time series as covariates. In this chapter, type-1 fuzzy functions approach has been applied to obtain forecasts of Australian beer consumption and Turkey electricity consumption time series data. The lagged variables of elementary time series have been used as covariates. The performance of type-1 fuzzy functions approach has been evaluated against some recent methods in the literature.

A few recurrent ANFIS approaches were proposed in the literature. Two main types of recurrences are possible in ANFIS architecture. Feedback can be made for input layer or right sides of Sugeno-type rules. In this study, a new type recurrent ANFIS is proposed for forecasting. Feedback mechanism is embedded to ANFIS by using squares of error terms as inputs in right sides of Sugeno-type fuzzy rules. The training of the proposed ANFIS is made by using particle swarm optimization technique. The proposed method was tested on some real world time series data and it is compared with some alternative forecasting methods in the literature. It was shown that the proposed method has the best forecasting performance.

Fuzzy time series approaches have been used for real world time series contain uncertainty. When these approaches are used, it is not necessary to satisfy the assumptions needed for conventional time series methods. Fuzzy time series methods are composed of three phases which are fuzzification, determination of fuzzy relations, and defuzzification. Artificial intelligence algorithms are widely employed in these phases. Genetic algorithm and differential evolution algorithm are one of the most popular artificial intelligence algorithms. Besides, the hybrid algorithms by obtaining the composed of some artificial intelligence algorithms have been frequently used in the literature. In this paper, a hybrid method composed by genetic algorithm and differential evolution algorithms is proposed to find the optimal interval lengths. The hybrid method proposed in this paper has been applied to Canadian lynx data and its superior forecasting performance was shown when compared with those obtained by other techniques suggested in the literature.