Time series forecasting via computational intelligence methods

Information technologies have many improvements about data storage and its usage in the last decades and it will have more according to technological breakthroughs. Data storage and data obtaining will be much easier than now after the Internet of Things revolution. This revolution can call as differently according to governed country. It named as Industry 4.0 in Germany, the Factory of the Future in France and Italy and Catapult in United Kingdom. The data explosion will also make the data analysis techniques especially in forecasting more important. A forecast is a prediction of some future things or events. Forecasting is an important problem that link many fields such as economics, industry, environmental sciences and much more. Most of usage, the forecasting involves from the time series data. Many applications of forecasting about the business exploit daily, weekly, monthly or any defined interval of the data. These applications can be listed in the areas such as operations management, marketing, finance and risk management, economics, industrial process control and, demography. These are only a few where forecast is required to make good decisions. The forecast model always aims to represent best estimate of the future value of the variable of interest. As it might be expected, these forecasts are not always accurate. Therefore, there is a definition between estimated and real data values named as forecast error. Eventually, it is a good practice to accompany a forecast with an estimate of the error bounds to represent the interval about how large a forecast error might be expected. Prediction Interval (PI) and Confidence Interval (CI) are the most used ones for representing the errors. The CIs handle with the accuracy of the prediction of the regression while the PIs consider the accuracy with the prediction to the targets values. A PI is constructed from interval bound that covers the future unknown value with a prescribed probability called a confidence level. The availability of PIs allows the decision makers to quantify the level of uncertainty associated with the point forecasts. A relatively wide PI indicates the presence of high level of uncertainties in the underlying system operation. On the other hand, narrow PIs give the decision makers the opportunity to decide more confidently with less chance of confronting an unexpected condition in the future. This useful information can guide the decision makers to avoid the selection of risky actions under uncertain conditions. Thus, the construction of PIs has been a subject of much attention. Thus, different methods haven been proposed for the construction of PIs such as delta technique, Bayesian technique, bootstrap, mean-variance estimation, lower and upper bound estimation method. In this thesis, alternative approach to the error bounds will be represent. Fuzzy linguistic term generation and representation via Fuzzy Logic based Lower and Upper Bound Estimator (FLUBE) based Triangular Fuzzy Number (TFN) is presented to estimate the uncertainty in the forecast. As it can be noticed via the titles, the thesis mainly based on the fuzzy logic. Fuzzy logic has been successfully implemented in various engineering areas including control, robotics, image processing, decision-making, estimation and modelling. Therefore, the proposed representation includes two different methodologies which will give the opportunity to the decision maker to quantify the uncertainty of the point forecasts with linguistic terms which might increase the interpretability. Moreover, the proposed approaches will provide valuable information about the accuracy of the forecast by providing a relative membership degree with respect to the target data. The proposed approaches consist of two main phases, the offline FLUBE design and the online TFN generation part as Linguistic Generation and Representation Approach (LinGRA) and Enhanced Linguistic Generation and Representation Approach (ElinGRA). In the context of the thesis, firstly, the time series concept and its analysis methodologies are discussed in addition to the basic information of the forecasting. Time series concept is also a basis of forecasting especially in our daily life's events. Therefore, the components and characteristics of the time series are handled to be a light for the time series analysis. The modelling techniques is the key factor of the forecasting models and the error evaluations of the forecasts. They are handled as concisely to give information as much as needed. Secondly, the error terms obtained from the real data values and the forecast models' outputs are modelled via the fuzzy modelling approach. Thanks to both fuzzy model, the error bounds can shape as nonlinear and nonsymmetrical conversely the classical erro bounds like PI. Furthermore, the forecasting error bounds, fuzzy logic systems, fuzzy time series and fuzzy modelling approaches are introduced as the basis of the proposed linguistic term generation approaches. The methodologies have differences on the determination of the linguistic terms phase that also illustrated as comparatively. Finally, the linguistic forecast generation approaches are used on the several data sets in comparison with conventional PI bounds to prove the efficiency. The methodologies can also follow at the part named as experimental results. Thanks to the membership degree of the proposed linguistic terms, the error evaluation of the forecast can be done with fuzzy numbers. Rather than the classical PIs, the proposed bounds utilize the realized value of the project not only bound-in or out consideration but also grading the forecast via the triangular fuzzy numbers. Therefore, the decision can have the opportunities to critize the last forecasts and their methods.