Multivariate Fuzzy Time Series Research Articles

Multi-rule combination prediction of compositional data time series based on multivariate fuzzy time series model and its application

Compositional data (CoDa) is a type of relative data reflecting the proportion of different units in an integrated system, which can reveal the internal structure of observed objects and has been widely used to analyze practical economic and management problems. However, the summation constraint limits the prediction of compositional data time series. Especially, with small samples and poor information characteristics of the data set, the difficulties are further exacerbated. Compared with real-valued time series analysis, fuzzy time series (FTS) mainly transforms initial observed data to be different status so that the historical evolution rules can be derived. As a result, forms of initial observed data can be concealed. Correspondingly, this paper aims to establish a multi-rule combination prediction of compositional data based on a multivariate fuzzy time series model, named GA-CoDa-MFTS. Firstly, with the interaction of components, the adjustment rules between components are explored by using the fuzzy logical relationship (FLR). Secondly, the Genetic algorithm (GA) is used to find the optimal weight of the predicted values under different rules and derive the combined predicted values. Finally, the prediction effectiveness of the model is verified by CRMSE and CMAPE through a numerical study.

Multi-output time series forecasting with randomized multivariate Fuzzy Cognitive Maps

Fuzzy Cognitive Maps (FCMs) have become a relevant technique for modeling and forecasting time series due to their advantages in dealing with uncertainty and simulating the dynamics of complex systems. Although numerous univariate and multivariate FCM-based forecasting models have been presented in the literature, one of the still open questions is how to enable FCMs to forecast multivariate time series for multiple-input, multiple-output (MIMO) systems with an efficient learning mechanism. from a computational point of view. This paper suggests a randomized MIMO FCM-based forecasting approach called MO-RHFCM to predict low-dimensional multivariate time series. More specifically, MO-RHFCM is a hybrid model merging the concepts of multivariate fuzzy time series, high order FCM (HFCM), and Echo State Networks (ESN). The structure of MO-RHFCM consists of three layers: input layer, reservoir (internal) layer, and output layer. Only the output layer is trainable using the Least Squares minimization algorithm; hence training the proposed MO-RHFCM method is fast and simple. The weights inside each sub-reservoir are selected randomly and remain fixed during the training process. The obtained results indicate the efficacy and validity of the proposed MO-RHFCM technique compared with some machine learning and deep learning baseline models.

A solar radiation intelligent forecasting framework based on feature selection and multivariable fuzzy time series

Accurate solar radiation forecasting can effectively improve solar energy utilization efficiency and decrease the operational cost of solar photovoltaic power plants. However, some common forecasting methods have certain limitations, such as neglecting data fuzziness, meteorological factors, feature selection, and seasonal adjustment. Therefore, a solar radiation intelligent forecasting framework based on feature selection and multivariable fuzzy time series is proposed. Specifically, a combined fuzzy strategy is used to fuzzy the data, and an improved multi-objective optimization algorithm is proposed to search for the optimal parameters. A seasonal multivariable fuzzy time series is proposed to achieve multivariable inputs and seasonal adjustments. The experimental analysis, statistical test, and robustness analysis all verify the superiority of the proposed forecasting framework compared with competitive models. The MAPE values of the proposed forecasting framework for two regions are about 6% and 4%, respectively, which outperform some common basic models such as BPNN(about 11% and 9%), ELM(about 12% and 10%), LSTM(about 9% and 7%). The comparison analysis further indicates that the vital parts of the forecasting framework containing feature selection, seasonal adjustment, multi-objective optimization, and multivariable inputs can all have a positive influence on forecasting performance.

Forecasting stock prices based on multivariable fuzzy time series

<abstract><p>With the development of the stock market, the proportion of the stock assets in the asset structure of the residents increases rapidly. Therefore, the research on the prediction of stocks has great theoretical significance and application potential. A key point of researching stock prices is how to pick out the main factors. In this study, principal component analysis (PCA) is applied to find out the main factors which mainly affect the stock price. Then an improved cluster analysis algorithm is proposed to fuzzy the data, and a qualitative analysis method is given to find the most suitable prediction set from the multiple fuzzy sets corresponding to the current fuzzy set. We also extend the inverse fuzzy number formula to a more general form to get the predicted value. Finally, Xishan Coal and Electricity Power (XSCE) and Taiwan Futures Exchange (TAIFEX) time series are predicted, using the proposed multivariate fuzzy time series method. The results show that the prediction error is lower than that of the previous models. The proposed method produces better forecasting performance.</p></abstract>

An improved monarch butterfly optimization based multivariate fuzzy time series approach for forecasting GDP of India

An improved monarch butterfly optimization based multivariate fuzzy time series approach for forecasting GDP of India

Evolving fuzzy time series for spatio-temporal forecasting in renewable energy systems

Forecasting in Renewable Energy Systems is a challenging problem since their inputs present some uncertainties in the data distribution. On the other hand, there is an increasing volume of information recorded by such systems that can be explored by a forecasting model with the expectation of improved performance. This work introduces e-MVFTS (evolving Multivariate Fuzzy Time Series), an evolving forecasting model based on Fuzzy Time Series, and an evolving clustering method based on TEDA (Typicality and Eccentricity Data Analytics) Framework, which uses multivariate time series in a spatio-temporal context. The model has an adaptation mechanism to deal with changes in the data distribution or concept drifts in data streams. The evolving clustering method is adjusted as the data points arrive and are processed, in an online manner. Its performance is evaluated in the application to problems of solar and wind energy forecasting as well as concept drift events. The model was developed in Python programming language using pyFTS library. To contribute to the replication of all the results, we provide all source codes in a public repository. The good results in the different experiments enable the e-MVFTS model to be used in forecasting problems with streaming data in renewable energy systems.

Distributed Evolutionary Hyperparameter Optimization for Fuzzy Time Series

Time series forecasting is an essential task in the management of Smart Cities and Smart Grids, becoming even more challenging when it needs to deal with big data time series. The development of highly accurate machine learning models is yet harder when considering the optimization of hyperparameters, which is an expensive computational task. To tackle these challenges this work proposes the Distributed Evolutionary Hyperparameter Optimization (DEHO) for the Weighted Multivariate Fuzzy Time Series method (WMVFTS), a simple and non-parametric forecasting method with high scalability and accuracy, comprising a sequential training and forecasting procedure and a MapReduce extension for distributed processing. The proposed methods were evaluated using a cluster with commodity hardware and two big time series, showing increasing speed up for training and test times as new CPU cores are added to cluster. Then the DEHO method was executed in the computational cluster, achieving fast convergence and feasible processing time and generating highly accurate WMVFTS models.

Information Systems of Forecasting Incidence Rates of Dengue Fever Disease Using Multivariate Fuzzy Time Series

Demak Regency is one of the regions in Central Java Province with a low incidence of Dengue Fever compared to other cities and districts. Even so, DHF control needs to be done to minimize the occurrence of dengue fever, because DHF is a fairly dangerous disease. One form of controlling the number of DHF events that is widely used is using forecasting models, one of them is using Fuzzy Time Series. The Multivariate Fuzzy Time Series (MFTS) model is a development of the Fuzzy Time Series model that can be used to forecast using time series data by using more than one variable for forecasting, compared to the Fuzzy Time Series method that usually using only one variable. Based on the research results obtained, the MFTS model has a fairly accurate MAPE value, wherein the best MAPE was at 3 years scenario with MAPE 10,728%.

A Multivariate Fuzzy Time Series Resource Forecast Model for Clouds using LSTM and Data Correlation Analysis

Today, almost all clouds only offer auto-scaling functions using resource usage thresholds, which are defined by users. Meanwhile, applying prediction-based auto-scaling functions to clouds still faces a problem of inaccurate forecast during operation in practice even though the functions only deal with univariate monitoring data. Up until now, there are still very few efforts to simultaneously process multiple metrics to predict resource utilization. The motivation for this multivariate processing is that there could be some correlations among metrics and they have to be examined in order to increase the model applicability in fact. In this paper, we built a novel forecast model for cloud proactive auto-scaling systems with combining several mechanisms. For preprocessing data phase, to reduce the fluctuation of monitoring data, we exploit fuzzification technique. We evaluate the correlations between different metrics to select suitable data types as inputs for the prediction model. In addition, long-short term memory (LSTM) neural network is employed to predict the resource consumption with multivariate time series data at the same time. Our model thus is called multivariate fuzzy LSTM (MF-LSTM). The proposed system is tested with Google trace data to prove its efficiency and feasibility when applying to clouds.

A novel forecasting method based on multi-order fuzzy time series and technical analysis

Financial trading is one of the most common risk investment actions in the modern economic environment because financial market systems are complex non-linear dynamic systems. It is a challenge to develop the inherent rules using the traditional time series prediction technique. In this paper, we proposed a new forecasting method based on multi-order fuzzy time series, technical analysis, and a genetic algorithm. Multi-order fuzzy time series (first-order, second-order and third-order) are applied in the proposed algorithm, and to improve the performance, genetic algorithm is used to find a good domain partition. Technical analysis such as the Rate of Change (ROC), Moving Average Convergence/Divergence (MACD), and Stochastic Oscillator (KDJ) are introduced to construct multi-variable fuzzy time series, and exponential smoothing is used to eliminate noise in the time series. In addition to the root mean square error and mean square error, the directional accuracy rate (DAR) is also used in our empirical studies. We apply the proposed method to forecast five well-known stock indexes and the NTD/USD exchange rates. Experimental results demonstrate that our proposed method outperforms other existing models based on fuzzy time series.

A clustering based forecasting algorithm for multivariable fuzzy time series using linear combinations of independent variables

There are two popular types of forecasting algorithms for fuzzy time series (FTS). One is based on intervals of universal sets of independent variables and the other is based on fuzzy clustering algorithms. Clustering based FTS algorithms are preferred since role and optimal length of intervals are not clearly understood. Therefore data of each variable are individually clustered which requires higher computational time. Fuzzy Logical Relationships (FLRs) are used in existing FTS algorithms to relate input and output data. High number of clusters and FLRs are required to establish precise input/output relations which incur high computational time. This article presents a forecasting algorithm based on fuzzy clustering (CFTS) which clusters vectors of input data instead of clustering data of each variable separately and uses linear combinations of the input variables instead of the FLRs. The cluster centers handle fuzziness and ambiguity of the data and the linear parts allow the algorithm to learn more from the available information. It is shown that CFTS outperforms existing FTS algorithms with considerably lower testing error and running time.

PERAMALAN JUMLAH WISATAWAN AUSTRALIA YANG BERKUNJUNG KE BALI MENGGUNAKAN MULTIVARIAT FUZZY TIME SERIES

The aim of this paper is to forecast the numbers of Australian tourist to Bali using multivariate fuzzy time series method (MFTS). MFTS method is development from fuzzy time series (FTS). The defferent betwen FTS and MFTS method is showed by factor in used. In FTS method using one factor, but in MFTS method using more than one factor. In this peper there was three factor used in this research, it was number of Australian tourist, Indonesian Inflation, and change rate of AUD to IDR. At the beginning, the speed of each factor was calculated. For each factor given weight, 0,999 for numbers of Australian tourist, -0,90 for Indonesian inflation, and 0,21 for change rate of AUD to IDR. The result showed that Australian tourist at July 2014 would visit Bali as much 91.056 tourist, with average error rate 6.87%.

A novel multivariate fuzzy time series based forecasting algorithm incorporating the effect of clustering on prediction

Forecasting has often played predominant roles in daily life as necessary measures can be taken to bypass the undesired and detrimental future prompted by this fact, the issue of forecasting becomes one of the most important topics of research for the modern scientists and as a result several innovative forecasting techniques have been developed. Amongst various well-known forecasting techniques, fuzzy time series-based methods are successfully used, though they are suffering from some serious drawbacks, viz., fixed sized intervals, using some fixed membership values (0, 0.5, and 1) and moreover, the defuzzification process only deals with the factor that is to be predicted. Additionally, most of the existing and widely used fuzzy time series-based forecasting algorithms employ their own clustering techniques that may be data-dependent and in turn the predictive accuracy decrease. Prompted by the fact, the present author developed a novel multivariate fuzzy forecasting algorithm that is able to remove all the drawbacks as also can predict the future occurrences with better predictive accuracy. Moreover, the comparisons with the thirteen other existing frequently used forecasting algorithms (viz., conventional, fuzzy time series-based algorithms and ANN) were performed to demonstrate its better efficiency and predictive accuracy. Towards the end, the applicability and predictive accuracy of the developed algorithm has been demonstrated using three different data sets collected from three different domains, such as: oil agglomeration process (coal washing technique), frequently occurred web error prediction and the financial forecasting. The real dataset related to oil agglomeration was collected from CIMFER, Dhanbad, India, that regarding the frequently occurred web error codes of www.ismdhanbad.ac.in, the official website of ISM Dhanbad, was collected from the Indian School of Mines (ISM) Dhanbad, India server and the finance data set was collected from the Ministry of Statistical and Program Implementation (Govt. of India).

On A New Framework of Autoregressive Fuzzy Time Series Models

Since its birth in 1993, fuzzy time series have seen different classes of models designed and applied, such as fuzzy logic relation and rule-based models. These models have both advantages and disadvantages. The major drawbacks with these two classes of models are the difficulties encountered in identification and analysis of the model. Therefore, there is a strong need to explore new alternatives and this is the objective of this paper. By transforming a fuzzy number to a real number via integrating the inverse of the membership function, new autoregressive models can be developed to fit the observation values of a fuzzy time series. With the new models, the issues of model identification and parameter estimation can be addressed; and trends, seasonalities and multivariate fuzzy time series could also be modeled with ease. In addition, asymptotic behaviors of fuzzy time series can be inspected by means of characteristic equations.

Prediction of stock index futures prices based on fuzzy sets and multivariate fuzzy time series

This paper makes a prediction of Chinese stock index (CSI) future prices using fuzzy sets and multivariate fuzzy time series method. We select Chinese CSI 300 index futures as the research object. The fuzzy time series model combines the fuzzy theory and the time series theory, thus this model can solve the fuzzy data in stock index futures prices. This paper establishes a multivariate model and improves the accuracy of computation. By combing traditional fuzzy time series models and rough set method, we use fuzzy c-mean algorithm to make the data into discrete. Further more, we deal with the rules in mature modules of the rough set and then refine the rules using data mining algorithms. Finally, we use the CSI 300 index futures to test our model and make a prediction of the prices.

A high-order multi-variable Fuzzy Time Series forecasting algorithm based on fuzzy clustering

A High–order algorithm for Multi-Variable Fuzzy Time Series (HMV-FTS) is presented based on fuzzy clustering to eliminate some well-known problems with the existing FTS algorithms. High-order algorithms can handle only one-variable FTS and multi-variable algorithms can handle only one-order FTS. HMV-FTS does both tasks simultaneously. FTS algorithms cannot incorporate existing information about future value of a variable in the forecasting process while HMV-FTS can. Defuzzification of the fuzzy value of a forecast to cluster centers or midpoint of intervals and use of intervals are other controversial problems with the existing FTS algorithms. These are eliminated by constructing fuzzy sets from partition matrices and letting each data point to contribute in defuzzification based on its membership grade in the fuzzy sets. In multi-variable FTS algorithms, one variable is considered as main variable which is forecasted and the other variables are secondary; while HMV-FTS treats all variables equally and more than one variable can be forecasted at the same time. It is shown that HMV-FTS is suitable for system identification, forecasting and interpolation. This algorithm is more accurate than popular FTS algorithms and other forecasting tools and systems such as ANFIS, Type II fuzzy model and ARIMA model.

A New Method for Short Multivariate Fuzzy Time Series Based on Genetic Algorithm and Fuzzy Clustering

Forecasting activities play an important role in our daily life. In recent years, fuzzy time series (FTS) methods were developed to deal with forecasting problems. FTS attracted researchers because of its ability to predict the future values in some critical situations where most standard forecasting models are doubtfully applicable or produce bad fittings. However, some critical issues in FTS are still open; these issues are often subjective and affect the accuracy of forecasting. In this paper, we focus on improving the accuracy of FTS forecasting methods. The new method integrates the fuzzy clustering and genetic algorithm with FTS to reduce subjectivity and improve its accuracy. In the new method, the genetic algorithm is responsible for selecting the proper model. Also, the fuzzy clustering algorithm is responsible for fuzzifying the historical data, based on its membership degrees to each cluster, and using these memberships to defuzzify the results. This method provides better forecasting accuracy when compared with other extant researches.

A Two Phase Algorithm for Fuzzy Time Series Forecasting using Genetic Algorithm and Particle Swarm Optimization Techniques

ABSTRACT Fuzzy Time series is being used for forecasting since last two decades for forecasting. Nature inspired computing techniques like other domains are now being used for optimization purpose in Fuzzy Time Series forecasting models to get improved results. In this paper we have presented a new algorithm for multivariate fuzzy time series forecasting having two phases. Genetic Algorithm and Particle Swarm Optimization techniques are used in this algorithm for optimization. We applied our algorithm on Taiwan forex Exchange (TAIFEX) index and got better results and minimized error rate as compared to previous methods. General Terms Nature inspired computing; Time Series forecasting Keywords Fuzzy time series; two-factor high-order fuzzy logical relationships; Genetic Algorithm, Particle Swarm Optimization; TAIFEX index. 1. INTRODUCTION Forecasting is prediction of unseen values of some sequence. It holds significance in economic and financial modeling as entrepreneurs use predicted values for business planning and taking key decisions. In the last two decades Fuzzy Time Series (FTS) is being used for forecasting purpose. Song and Chissom [1, 2] used the concept of FTS and forecasted number of enrollments of the University of Alabama. Many other researchers proposed their models for enrollments forecasting of the University of Alabama ([3], [4], [5], [6], [7], [8], [9], [10] and [11]), temperature prediction [12, 13] and car road accidents [14, 15] using fuzzy time series. Huarng [7] presented heuristic based model for fuzzy time series forecasting. Jilani and Burney [14] presented M-factor high order fuzzy time series forecasting model for car road accident data. Jilani and Burney [16] presented new heuristic based approach for frequency density based partitioning for fuzzy time series forecasting of stock market. In the recent years many researchers started applying Nature inspired computation (NIC) techniques for optimization purpose in FTS forecasting. Kuo et al. [17] and Huang et al.[18] proposed Particle Swarm Optimization (PSO) based FTS forecasting models for enrollments data of the University of Alabama. Park et al. [19] proposed a forecasting model for TAIFEX and KOSPI-200 index, which was based on FTS and swarm intelligence. Jilani et. al. [20] proposed a PSO based FTS forecasting model for car road accidents. Jilani et. al. presented a hybrid algorithm based on Genetic Algorithm (GA) and PSO for forecasting TAIFEX Genes are randomly generated initially to make chromosomes and KSE-100 index. Jilani et. al. [22] presented a trend based heuristic approach using GA for forecasting car road accidents. In this paper we have applied genetic algorithm in first phase to optimize weights, and in second phase we used those weights and optimized interval length to get best forecasting result.

Penerapan Logika Fuzzy Dalam Pemodelan Perkiraan Tingkat Inflasi Di Indonesia

Modeling for inflation rate in Indonesia was done by some researcher with conventional model. The conventional model can not be applied if the data are linguistic variables. Fuzzy system can be used to overcome the weak of this method. The goal of this research is to establish the model for forecasting inflation rate in Indonesia based on fuzzy time series data. In this research, forecasting inflation rate use table look up scheme method based on multivariate fuzzy time series data. This research is done by the following steps: 1) determine input-output data; 2) determine fuzzification for input-output data; 3) determine fuzzy rules base by table lookup scheme method; 4) construct fuzzy inference engine; 5) construct defuzzification; 6) construct fuzzy system for modeling inflation rate in Indonesia; 7) determine validation for model used MSE criteria. The results of this research are 1) we develop 8 fuzzy models; 2) The model with Gaussian membership function, minimum inference engine, 25 fuzzy rules has minimum MSE value, 5.5671. Therefore this model can be used to predict inflation rate in Indonesia based on inflation previously , credit interest rate, money supply, gross national product and exchange rate of Rupiah.

A Particle Swarm Intelligence Based Fuzzy Time Series Forecasting Model

In this paper, we have presented a new particle swarm optimization based multivariate fuzzy time series forecasting method. This method assumes five-factors with one main factor of interest. History of past three years is used for making new forecasts. This new method is applied in forecasting total number of car accidents in Belgium using four secondary factors. We also make comparison of our proposed method with existing methods of fuzzy time series forecasting. Experimentally, it is proved that our proposed method perform better than many existing fuzzy time series forecasting methods. The interest of this paper centers in applying swarm intelligence approaches in forecasting related problems. The dataset is taken from National Institute of Statistics, Belgium.