A Comparative Study on Fuzzy Time Series Forecasting and Autoregressive Integrated Moving Average Models

To ensure the sustainable development of an enterprise, it is necessary to properly analyze the enterprise development, to ground the plans and management decisions on effective diagnostics and prediction of current and future economic situation at the enterprise. The article presents a study on the application of fuzzy time series forecasting methods. A new approach is applied to forecasting an enterprise's net income using a fuzzy technique. For testing the methodology, there were used statistical data on the enterprise net income level of the Ukrainian enterprise from 2002 to 2017. In the method of Stevenson and Potter, it is proposed to use as the universe of discourse, in the process of applying the method for all defined fuzzy sets, the intervals of variation of such indicator as growth rate. The same background as in Stevenson and Porter’s model is used in this article for forecasting the time series levels using the growth rates of the actual data as the universe of discourse. The forecasting results, obtained by this approach, are supposed to have more accuracy rate than other fuzzy time series models. Some modifications of this technique are proposed to obtain a higher accuracy rate and a point forecast one step forward.

Background: One forecasting method that is often used is time series forecasting. The development of applied mathematics has encouraged new mathematical findings that led to the birth of new branches of mathematics, one of which is fuzzy. Purpose: The objectives of the study, namely forecasting, fuzzy set, time series, fuzzy time series, fuzzy time series Singh, interval ratio and measurement of accuracy level. Method: This research method applies Chen's fuzzy time series in the section of determining the universe of talk you to the fuzzification of historical data and in the part of forecasting results obtained through a heuristic approach by building three forecasting rules, namely Rule 2.1, Rule 2.2, and Rule 2.3 to obtain better results and affect very small AFER values. As well as making modifications to the interval partition section using interval ratios to be able to reflect data variations. Results: Based on the calculation of AFER values for order 2, order 3, and order 4 respectively obtained at 1.06389%, 0.689368%, and 0.711947%. Therefore, it can be said, Singh's fuzzy time series forecasting method based on the ratio of 3rd-order intervals is better than that of 2nd-order and 4th-order. Conclusion: Based on the results of research and discussion that has been carried out, it can be concluded that Singh's fuzzy time series forecasting method has the same algorithm as fuzzy time series forecasting. Singh's fuzzy time series forecasting method based on interval ratios applies fuzzy time series and Singh forecasting. Singh's fuzzy time series forecasting modification accuracy rate based on interval ratios produces excellent forecasting values according to evaluator average forecasting error rate (AFER).

n the literature, there have been a good many different forecasting methods related forecasting problems of fuzzy time series. The main issue of fuzzy time series forecasting is the accuracy of the forecasted values. The forecasting accuracy rate is affected by the length of each interval in the universe of discourse. Thus, it is substantial to determine the length of each interval. In this study, new computational method based on class width to determine interval length is proposed and also used coefficient of variation for time series forecasting. After the intervals are formed, the historical time series data set is fuzzified according to fuzzy time series theory. The proposed model has been tested on the student enrollments, University of Alabama and a real life problem of rice production for containing higher uncertainty. This method was compared with existent methods to determine the effectiveness in terms of the mean square error (MSE) and the average forecasting (AFE). The results are shown that the proposed model can achieve a higher forecasting accuracy rate than the existent models.

About the research of fuzzy time series model are proposed by Song and Chissom(1993). There are many researchers have proposed many different methods and models. Example the p-order fuzzy time series model FAR(p), the p-order fuzzy time series model with fuzzy trend, and the p-order fuzzy seasonal time series model FSAR(p)s. But, about a fuzzy time series has shown a tendency to increase or decrease over a particular period and also to follow a seasonal pattern, FASRI(p, d)×(P, D)(subscript s) that is no any paper to research this topic. In this research, we want to study the FASRI(p, d)×(P, D)(subscript s) model of fuzzy time series. First, we make testing for the fuzzy trend of fuzzy time series by the rule of Liaw(2000) proposed. If the fuzzy time series with fuzzy trend, we make a differencing for the original time series, then make testing for the fuzzy seasonal of the new fuzzy time series by the rule of Liaw(2000) proposed. If the new fuzzy time series with fuzzy seasonal. It is told us the fuzzy time series simultaneous with fuzzy trend and fuzzy seasonal. We must consider the fuzzy time series simultaneous with fuzzy trend and fuzzy seasonal at the model construction. Finally, we use two relevant instances verify our propose method.

The arising air pollution has addressed much attention globally due to its detrimental effects on human health and environment. As an early warning system for air quality control and management, it is important to provide precise information about the future concentrations in pollutants. We present here a time series model in predicting the Air Pollution Index (API) from three different stations; industrial, residential, and sub-urban areas between 2000 and 2009. In this paper, the Box–Jenkins approach of seasonal autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and three models of fuzzy time series (FTS) have been compared by using the mean absolute percentage error, mean absolute error, mean square error, and root mean square error. Although all the methods were used as operational tools, the ANN seemed more accurate in forecasting API. The results showed that FTS (i.e. Chen’s, Yu’s, and Cheng’s) performed inconsistent results since the conventional methods of ARIMA outperformed the performance of FTS. However, consistent results were achieved as the ANNs gave the smallest forecasting error compared to FTS and ARIMA.

This paper proposes a novel optimized model based on the combination of the fuzzy time series (FTS) method and Jacobi polynomials for predicting the behavior of fiber-reinforced polymer (FRP)-confined concrete under compression loads. In this model, the stress-strain curves are approximated by Jacobi polynomials. Then, the FTS method is used to develop a nonlinear relationship between the coefficients of Jacobi polynomials and the specimen features. Moreover, another FTS model is developed to predict the ultimate stress and the ultimate strain of FRP-confined concrete. A comparative analysis is performed to demonstrate the effectiveness of the proposed model. As compared with the well-known design-oriented models applied to 69 experiments, the root mean square error is decreased more than 50% by the proposed model. Also, the effects of input features on the physical behavior of the specimens as described by the proposed model are consistent with the relevant theories and experiments.

Enrolment forecasting, which provides information for decision making and budget planning, is important in many ways to higher education. Because of its importance, researchers have proposed many forecasting methods to improve accuracy. Different methods such as genetic algorithm, least square that are used to forecast enrolment of student do not give relatively accurate results. However, obtaining accuracy is not an easy task, as many factors have impacts on enrolment numbers. In this work, a fuzzy time series was developed for efficient enrolment forecasting. The model is made up of four steps which are definition of the universe of discourse and intervals, fuzzification of historical data, establishment of fuzzy relationships and enrolment forecast. The max-min operator was used as universe of discourse and we compared our proposed method with the existing linear regression method. The historical enrolment figures of the University of Agriculture, Abeokuta were used as a data set for testing and were implemented using Visual Basic. The forecasting result of the fuzzy time series method is compared with that of the existing least square method, the fuzzy time series method produces the smallest values of the mean square error (MSE) as compared with the least square method. The application was also used to predict students’ enrolment for the next five years. The proposed method was found to obtain more accurate forecasting results than the existing method.

Fuzzy time series methods have been applied to social forecasting for over a decade; however, little research has been done to discuss the decision of an optimal fuzzy model for time series. In the paper, we evaluate the forecasting performance of three listed multivariate fuzzy models by comparing forecasting MSE of model. The data obtained from AEROM, Taiwan, includes Taiwan’s exports and foreign exchange rate for models’ test. The algorithm for predictive value of the models has three-stage computation procedure: First, calibrating time series correlation, deciding window base and interval partition; second, solving the static forecasting value of each model; third, comparing the dynamic parameter to impact of the forecasting error. The empirical results indicate that increasing predictor variables has no significant effect on predictive performance of the models; increasing length of interval would not improve the prediction performance of the models. Moreover, Fuzzy model is better for short-term time series forecasting. For forecasting purpose, Heuristic model has best forecasting performance among three fuzzy models. The findings of the paper represent a significant contribution to our understanding of the applicability of fuzzy models to predict.

A new approach based on artificial neural networks for high order multivariate fuzzy time series

Non-stationary time series plays a prominent role in the analysis of performance time series of many real-world systems. Recently, fuzzy time series models have been extended to forecast non-stationary time series. Over different phases of time, performance time series may show drastic changes. Therefore, a non-stationary time series is partitioned according to different phases of time. These phases may be taken as weeks, months, or years. Over different phases of time, the universe of discourse, knowledge base, and rule base may vary. A common constraint in the modelling of time-variant fuzzy time series is their incapability to address the phase change of time in the model and accordingly incorporate the necessary changes in the universe of discourse, knowledge base, and rule base over different time phases. To address this issue, a Phase-cum-Time Variant Fuzzy Time Series Model (PTVFTS) is presented in this paper. The PTVFTS model is developed so that it will address the problem of phase change as well as the time variations within each phase simultaneously. The concept of the model rebuilding process is applied to handle changes over each phase and the modified parameter adaptation technique is used for the time variations within each phase. The developed model is applied to the daily closing price time series for the years 2017, 2018, 2019, 2020, 2021, and 2022 separately of stock market indices, NASDAQ, S&P 500, Dow Jones, and TAIEX. The comparison of the developed model is made with the time-variant fuzzy time series model known as the non-stationary fuzzy time series model (NSFTS), Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) model, Long Short-Term Memory (LSTM) model, and the classical Auto-Regressive Integrated Moving Average (ARIMA) model. The efficiency of the developed PTVFTS model is tested using forecasting metrics and statistical tests. The comparison shows that the developed model is more efficient in forecasting phase-cum-time variant non-stationary time series.

Fuzzy time series model (FTS) has been widely used to forecast various time series data. When some data are missing, the forecasting accuracy will be greatly reduced. Therefore, a new forecasting method G-FTS is proposed based on the Gaussian mixture model and FTS. First, the distribution of the samples is estimated by using a Gaussian mixture model, the missing data are filled with the estimated distribution, and then a fuzzy time series forecasting is performed. The effectiveness of this method is illustrated by forecasting the monthly inventory data of small and medium-sized industrial enterprises in China. According to the characteristics of industrial data, such as time correlation, fast arrival, and large quantity, a dynamic forecasting method Dynamic-GFTS is proposed. This method is used to forecast the data collected by a textile factory. Simulation results show that Dynamic-GFTS is more effective in actual industrial data.

Triple exponential smoothing is one of the prominent linear models for seasonal time series forecasting. Fuzzy time series forecasting is originated as a new advent for forecasting the data which is imprecise and vague. In this work, we proposed a methodology using both triple exponential smoothing and fuzzy time series. It has the advantage of modelling aspects in linear and non-linear setup. Empirical results with real-world data sets show that the hybrid model is an efficient one based on forecasting accuracy than the component models used individually.KeywordsFuzzy time seriesHybridTriple exponential smoothing

Problem statement: Forecasting is very important in many types of organizations since predictions of future events must be incorporated into the decision-making process. In the case of tourism demand, better forecast would help directors and investors make operational, tactical and strategic decisions. Besides that, government bodies need accurate tourism demand forecasts to plan required tourism infrastructures, such as accommodation site planning and transportation development, among other needs. There are many types of forecasting methods. Generally, time series forecasting can be divided into classical method and modern methods. Recent studies show that the newer and more advanced forecasting techniques tend to result in improved forecast accuracy, but no clear evidence shows that any one model can consistently outperform other models in the forecasting competition. Approach: In this study, the performance of forecasting between classical methods (Box-Jenkins methods Seasonal Auto-Regressive Integrated Moving Average (SARIMA), Holt Winters and time series regression) and modern methods (fuzzy time series) has been compared by using data of tourist arrivals to Bali and Soekarno-Hatta gate in Indonesia as case study. Results: The empirical results show that modern methods give more accurate forecasts compare to classical methods. Chen’s fuzzy time series method outperforms all the classical methods and others more advance fuzzy time series methods. We also found that the performance of fuzzy time series methods can be improve by using transformed data. Conclusion: It is found that the best method to forecast the tourist arrivals to Bali and Soekarno-Hatta was to be the FTS i.e., method after using data transformation. Although this method known to be the simplest or conventional methods of FTS, yet this result should not be odd since several previous studies also have shown that simple method could outperform more advance or complicated methods.

Fu zzy time series forecasting methods have been widely studied in recent years. This is because fuzzy time series forecasting methods are co mpatib le with flexib le calculat ion techniques and they do not require constraints that exist in conventional time series approaches. Most of the real life time series exhibit periodical changes arising fro m seasonality. These variations are called seasonal changes. Although, conventional time series approaches for the analysis of time series which have seasonal effect are abundant in literature, the number of fuzzy t ime series approaches is limited. In almost all of these studies, membership values are ignored in the analysis process. This affects forecasting performance of the approach negatively due to the loss of information as well as posing a situation that is incompatible with the basic features of fuzzy set theory. In this study, for the first time in literature, a new seasonal fuzzy time series approach which considers membership values in both identificat ion of fuzzy relat ions and defuzzification steps was proposed. In the proposed method, we used fuzzy C-means clustering method in fuzzification step and artificial neural networks (ANN) in identification of fu zzy relation and defuzzification steps which consider membership values. The proposed method was applied to various seasonal fuzzy time series and obtained results were compared with some conventional and fuzzy time series approaches. In consequence of this evaluation, it was determined that forecasting performance of the proposed method is satisfactory.

Rice has become the main staple food for almost the entire population of Indonesia. However, in Indonesia, the price of food commodities (rice) often fluctuates in price. Due to the rapid fluctuation of rice prices and the uncertainty in the future, it is necessary to forecast rice prices. This study aims to predict the price of rice in the city of Mataram using the Holt double exponential smoothing method and the Cheng fuzzy time series. The model's performance is based on Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) indicators. Forecasting model based on Holt's double exponential smoothing method, the MSE value is 705967.4994 and the MAPE value is 7.91%. On the other hand, based on Cheng's fuzzy time series method, the performance of the forecasting model based on the MSE indicator is 566312.340 and based on the MAPE value of 6.75%. Based on these results, Cheng's fuzzy time series method is more accurate than Holt's double exponential smoothing method. Keywords: Double Exponential Smoothing Holt, Fuzzy Time Series Cheng, Rice Price, MAPE, MSE