The adaptive fuzzy time series model with an application to Taiwan’s tourism demand

In this study, an adaptive fuzzy time series model for forecasting Taiwan’s tourism demand is proposed to further enhance the predicted accuracy. We first transfer fuzzy time series data to the fuzzy logic group, assign weights to each period, and then use the proposed adaptive fuzzy time series model for forecasting in which an enrollment forecasting values is applied to obtain the smallest forecasting error. Finally, an illustrated example for forecasting Taiwan’s tourism demand is used to verify the effectiveness of proposed model and confirmed the potential benefits of the proposed approach with a very small forecasting error MAPE and RMSE.     

A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand

The fuzzy logical relationships and the midpoints of interval have been used to determine the numerical in-out-samples forecast in the fuzzy time series modeling. However, the absolute percentage error is still yet significantly improved. This can be done where the linguistics time series values should be forecasted in the beginning before the numerical forecasted values obtained. This paper introduces the new approach in determining the linguistic out-sample forecast by using the index numbers of linguistics approach. Moreover, the weights of fuzzy logical relationships are also suggested to compensate the presence of bias in the forecasting. The daily load data from National Electricity Board (TNB) of Malaysia is used as an empirical study and the reliability of the proposed approach is compared with the approach proposed by Yu. The result indicates that the mean absolute percentage error (MAPE) of the proposed approach is smaller than that as proposed by Yu. By using this approach the linguistics time series forecasting and the numerical time series forecasting can be resolved.     

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

基于直觉模糊线性方程组的IFTS 预测方法

针对模糊时间序列预测理论对不确定性数据集的实时模糊变化趋势研究存在的不足, 规范了直觉模糊时间序列的定义, 提出了基于直觉模糊线性方程组的直觉模糊时间序列预测方法. 所提出的算法将模型的求解转化为一系列带有约束的线性规划问题, 准确地反映了序列数据随时间发展变化的模糊关联规律, 简化了预测模型的复杂度, 提高了时间序列预测的精度, 扩展了直觉模糊时间序列预测理论的应用范围. 最后, 通过仿真实验验证了所提出方法的有效性和优越性.

     

基于区间相似度的模糊时间序列预测算法

针对现有模糊时间序列预测算法无法适应预测中新关系出现的问题,提出了一种基于区间相似度的模糊时间序列预测（ISFTS）算法。首先,在模糊理论的基础上,采用基于均值的方法二次划分论域的区间,在论域区间上定义相应模糊集将历史数据模糊化;然后建立三阶模糊逻辑关系并引入逻辑关系相似度的计算公式,计算未来数据变化趋势值得到预测的模糊值;最后对预测模糊值去模糊化得到预测的确定值。由于ISFTS算法是预测数据变化趋势,克服了目前预测算法的逻辑关系的缺陷。仿真实验结果表明,与同类的预测算法相比,ISFTS算法预测误差更小,在误差相对比(MAPE)、绝对误差均值(MAE)和均方根误差(RMSE)三项指标上均优于同类的对比算法,因此ISFTS算法在时间序列预测中尤其是大数据量情况下的预测具有更强的适应性。     

AN ADAPTIVE EXPECTATION GENETIC ALGORITHM BASED ON ANFIS AND MULTINATIONAL STOCK MARKET VOLATILITY CAUSALITY FOR TAIEX FORECASTING

The stock market is a highly complex and dynamic system, and forecasting stock is complicated and difficult. Successful prediction of stock prices may promise attractive benefits; therefore, stock market forecasting is important and of great interest. The economy of Taiwan relies on international trade deeply and the fluctuations of international stock markets impact Taiwan's stock market to certain degree. It is practical to use the fluctuations of other stock markets as forecasting factors for forecasting on the Taiwan stock market. Further, stock market investors usually make short-term decisions based on recent price fluctuations, but most time series models use only the last period of stock price in forecasting. In this article, the proposed model uses the fluctuations of other national stock markets as forecasting factors and employs an expectation equation method whose parameters are optimized by a genetic algorithm (GA) joined with an adaptive network–based fuzzy inference system (ANFIS) model to forecast the Taiwan stock index. To evaluate the forecasting performance, the proposed model is compared with Chen's model and Yu's model. The experimental results indicate that the proposed model is superior to the listing methods (Chen's model and Yu's model) in terms of root mean squared error (RMSE).     

High-precision forecast using grey models

In recent years the grey theorem has been successfully used in many prediction applications. The proposed Markov-Fourier grey model prediction approach uses a grey model to predict roughly the next datum from a set of most recent data. Then, a Fourier series is used to fit the residual error produced by the grey model. With the Fourier series obtained, the error produced by the grey model in the next step can be estimated. Such a Fourier residual correction approach can have a good performance. However, this approach only uses the most recent data without considering those previous data. In this paper, we further propose to adopt the Markov forecasting method to act as a longterm residual correction scheme. By combining the short-term predicted value by a Fourier series and a long-term estimated error by the Markov forecasting method, our approach can predict the future more accurately. Three time series are used in our demonstration. They are a smooth functional curve, a curve for the stock market and the Mackey-Glass chaotic time series. The performance of our approach is compared with different prediction schemes, such as back-propagation neural networks and fuzzy models. All these methods are one-step-ahead forecasting. The simulation results show that our approach can predict the future more accurately and also use less computational time than other methods do.     

两种时间序列模型在客流量预测上的比较

模糊时间序列模型和季节模型都是基于时间序列的模型,为了探讨在时间序列表现出一定的周期性时,哪种模型的预测效果会更好,分别利用模糊时间序列模型和季节模型对南京某商场的客流量进行预测,计算并比较两种方法下的相对误差值和RMSE（Root Mean Square Error）值,发现季节模型的相对误差值图形的平滑度要优于模糊时间序列模型,季节模型的RMSE值小于模糊时间序列模型,这表明考虑到数据特征的模型有更好的预测结果。     

Deterministic fuzzy time series model for forecasting enrollments

The fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data. There have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead. However, the issues of controlling uncertainty in forecasting, effectively partitioning intervals, and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated. This paper proposes a novel deterministic forecasting model to manage these crucial issues. In addition, an important parameter, the maximum length of subsequence in a fuzzy time series resulting in a certain state, is deterministically quantified. Experimental results using the University of Alabama’s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy, robustness, and reliability. Moreover, the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results.     

A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting

Time series forecasting is an important and widely popular topic in the research of system modeling, and stock index forecasting is an important issue in time series forecasting. Accurate stock price forecasting is a challenging task in predicting financial time series. Time series methods have been applied successfully to forecasting models in many domains, including the stock market. Unfortunately, there are 3 major drawbacks of using time series methods for the stock market: (1) some models can not be applied to datasets that do not follow statistical assumptions; (2) most time series models that use stock data with a significant amount of noise involutedly (caused by changes in market conditions and environments) have worse forecasting performance; and (3) the rules that are mined from artificial neural networks (ANNs) are not easily understandable.To address these problems and improve the forecasting performance of time series models, this paper proposes a hybrid time series adaptive network-based fuzzy inference system (ANFIS) model that is centered around empirical mode decomposition (EMD) to forecast stock prices in the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Hang Seng Stock Index (HSI). To measure its forecasting performance, the proposed model is compared with Chen's model, Yu's model, the autoregressive (AR) model, the ANFIS model, and the support vector regression (SVR) model. The results show that our model is superior to the other models, based on root mean squared error (RMSE) values.     

A hybrid ANFIS based on n-period moving average model to forecast TAIEX stock

Linear model is a general forecasting model and moving average technical index (MATI) is one of useful forecasting methods to predict the future stock prices in stock markets. Therefore, individual investors, stock fund managers, and financial analysts attempt to predict price fluctuation in stock markets by either linear model or MATI. From literatures, three major drawbacks are found in many existing forecasting models. First, forecasting rules mined from some AI algorithms, such as neural networks, could be very difficult to understand. Second, statistic assumptions about variables are required for time series to generate forecasting models, which are not easily understandable by stock investors. Third, stock market investors usually make short-term decisions based on recent price fluctuations, i.e., the last one or two periods, but most time series models use only the last period of stock price. In order to overcome these drawbacks, this study proposes a hybrid forecasting model using linear model and MATI to predict stock price trends with the following four steps: (1) test the lag period of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and calculate the last n-period moving average; (2) use subtractive clustering to partition technical indicator values into linguistic values based on data discretization method objectively; (3) employ fuzzy inference system (FIS) to build linguistic rules from the linguistic technical indicator dataset, and optimize the FIS parameters by adaptive network; and (4) refine the proposed model by adaptive expectation models. The proposed model is then verified by root mean squared error (RMSE), and a ten-year period of TAIEX is selected as experiment datasets. The results show that the proposed model is superior to the other forecasting models, namely Chen's model and Yu's model in terms of RMSE.     

A spatio-temporal decomposition based deep neural network for time series forecasting

Spatio-temporal problems arise in a broad range of applications, such as climate science and transportation systems. These problems are challenging because of unique spatial, short-term and long-term patterns, as well as the curse of dimensionality. In this paper, we propose a deep learning framework for spatio-temporal forecasting problems. We explicitly design the neural network architecture for capturing various types of spatial and temporal patterns, and the model is robust to missing data. In a preprocessing step, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of the neural network. A fuzzy clustering method finds clusters of neighboring time series residuals, as these contain short-term spatial patterns. The first component of the neural network consists of multi-kernel convolutional layers which are designed to extract short-term features from clusters of time series data. Each convolutional kernel receives a single cluster of input time series. The output of convolutional layers is concatenated by trends and followed by convolutional-LSTM layers to capture long-term spatial patterns. To have a robust forecasting model when faced with missing data, a pretrained denoising autoencoder reconstructs the model’s output in a fine-tuning step. In experimental results, we evaluate the performance of the proposed model for the traffic flow prediction. The results show that the proposed model outperforms baseline and state-of-the-art neural network models.     

Fuzzy based trend mapping and forecasting for time series data

The study demonstrates the superiority of fuzzy based methods for non-stationary, non-linear time series. Study is based on unequal length fuzzy sets and uses IF-THEN based fuzzy rules to capture the trend prevailing in the series. The proposed model not only predicts the value but can also identify the transition points where the series may change its shape and is ready to include subject expert’s opinion to forecast. The series is tested on three different types of data: enrolment for Alabama university, sales volume of a chemical company and Gross domestic capital of India: the growth curve. The model is tested on both kind of series: with and without outliers. The proposed model provides an improved prediction with lesser MAPE (mean average percentage error) for all the series tested.     

A computational method of forecasting based on high-order fuzzy time series

This paper presents a computational method of forecasting based on high-order fuzzy time series. The developed computational method provides a better approach to overcome the drawback of existing high-order fuzzy time series models. Its simplicity lies with the use of differences in consecutive values of various orders as forecasting parameter and a w-step fuzzy predictor in place of complicated computations of fuzzy logical relations. The objective of the present study is to examine the suitability of various high-order fuzzy time series models in forecasting. The general suitability of the developed method has been tested by implementing it in the forecasting of student enrollments of the University of Alabama and in the forecasting of crop (Lahi) production, a case of high uncertainty in time series data. The results obtained have been compared in terms of average error of forecast to show superiority of the proposed model.     

An effective neural network and fuzzy time series-based hybridized model to handle forecasting problems of two factors

Fuzzy time series forecasting method has been applied in several domains, such as stock market price, temperature, sales, crop production and academic enrollments. In this paper, we introduce a model to deal with forecasting problems of two factors. The proposed model is designed using fuzzy time series and artificial neural network. In a fuzzy time series forecasting model, the length of intervals in the universe of discourse always affects the results of forecasting. Therefore, an artificial neural network- based technique is employed for determining the intervals of the historical time series data sets by clustering them into different groups. The historical time series data sets are then fuzzified, and the high-order fuzzy logical relationships are established among fuzzified values based on fuzzy time series method. The paper also introduces some rules for interval weighing to defuzzify the fuzzified time series data sets. From experimental results, it is observed that the proposed model exhibits higher accuracy than those of existing two-factors fuzzy time series models.     

FORECASTING FUZZY TIME SERIES ON A HEURISTIC HIGH-ORDER MODEL

ABSTRACT

Chen first proposed the high-order fuzzy-time series model to overcome the drawback of existing fuzzy first-order forecasting models. His model involved easy calculations and forecasted more accurately than the other models. This study proposes an enhanced fuzzy-time series model, called heuristic high-order fuzzy time series model, to deal with forecasting problems. The proposed model aims to overcome the deficiency of Chen's model, which depends strongly on the highest-order fuzzy-time series to eliminate ambiguities at forecasting and requires a vast memory for data storage. The empirical analysis reveals that the proposed model yields more accurate forecasts.     

INTUITIONISTIC FUZZY SETS BASED METHOD FOR FUZZY TIME SERIES FORECASTING

Fuzzy time series models are of great interest in forecasting when the information is imprecise and vague. However, the major problem in fuzzy time series forecasting is the accuracy of the forecasted values. In the present study we propose a hybrid method of forecasting based on fuzzy time series and intuitionistic fuzzy sets. The proposed model is a simplified computational approach that uses the degree of nondeterminacy to establish fuzzy logical relations on time series data. The developed model was implemented on the historical enrollment data for the University of Alabama and the forecasted values were compared with the results of existing methods to show its superiority. The suitability of the proposed method was also examined in forecasting market share prices of the State Bank of India on the Bombay Stock Exchange, India.     

A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan

This paper proposes a hybrid methodology that exploits the unique strength of the seasonal autoregressive integrated moving average (SARIMA) model and the support vector machines (SVM) model in forecasting seasonal time series. The seasonal time series data of Taiwan’s machinery industry production values were used to examine the forecasting accuracy of the proposed hybrid model. The forecasting performance was compared among three models, i.e., the hybrid model, SARIMA models and the SVM models, respectively. Among these methods, the normalized mean square error (NMSE) and the mean absolute percentage error (MAPE) of the hybrid model were the lowest. The hybrid model was also able to forecast certain significant turning points of the test time series.     

基于改进狼群算法的模糊时间序列预测模型

当使用模糊时间序列预测模型进行预测时, 模糊区间的不同划分对最后的预测精度有着十分重要的影响. 针对如何更有效的划分模糊区间、进一步提高模糊时间序列的预测精度问题, 本文提出了一种基于改进狼群算法 的模糊时间序列预测模型. 为此首先简要介绍了模糊时间序列, 然后阐述了狼群算法并在其游走行为中引入趋向 行为和死亡概率对其进行了改进, 最后利用改进狼群算法来划分模糊区间, 建立了一种新的模糊时间序列预测模 型. 将Alabama大学入学人数作为实验数据进行实例分析和验证. 通过与现有的一些模型进行对比分析, 本文所提 模型具有更高的预测精度, 为模糊时间序列预测提供了新思路.     

A hybrid model based on adaptive-network-based fuzzy inference system to forecast Taiwan stock market

In recent years, many academy researchers have proposed several forecasting models based on technical analysis to predict models such as Engle, 1982, Cheng et al., 2010. After reviewing the literature, two major drawbacks are found in past models: (1) the forecasting models based on artificial intelligence algorithms (AI), such as neural networks (NN) and genetic algorithms (GAs), produce complex and unintelligible rules; and (2) statistic forecasting models, such as time series, require some basic assumptions for variables and build forecasting models based on mathematic equations, which are not easily understandable by stock investors. In order to refine these drawbacks of past models, this paper has proposed a model, based on adaptive-network-based fuzzy inference system which uses multi-technical indicators, to predict stock price trends. Three refined processes have proposed in the hybrid model for forecasting: (1) select essential technical indicators from popular indicators by a correlation matrix; (2) use the subtractive clustering method to partition technical indicator value into linguistic values based on an data discretization method; (3) employ a fuzzy inference system (FIS) to extract rules of linguistic terms from the dataset of the technical indicators, and optimize the FIS parameters based on an adaptive network to produce forecasts. A six-year period of the TAIEX is employed as experimental database to evaluate the proposed model with a performance indicator, root mean squared error (RMSE). The experimental results have shown that the proposed model is superior to two listing models (Chen’s and Yu’s models).