Fuzzy Time Series Model Research Articles

EXCHANGE RATE FORECASTING USING FUZZY TIME SERIES-MARKOV CHAIN

Exchange rate forecasting plays an important role in financial management. However, it is a complex process with high nonlinearity and data irregularity. Moreover, the forecasting of exchange rate is highly involved with imprecise and uncertain data. Analysis of forecasting models which corresponds to the exchange rate has always experienced fluctuations. Therefore, exchange rate forecasting becomes a challenging task in finance. Several studies have shown that stand-alone forecasting models such as time series, fuzzy time series, and Markov chain have their own drawbacks and are not successful enough in forecasting accurately. In this study, we propose a hybrid model of fuzzy time series-Markov chain to forecast the future exchange rate. Fuzzy time series-Markov chain is a combination of the classic fuzzy time series model with Markov chain model used to analyse a set of time series data. The main motivation for this study is to improve the accuracy in exchange rate forecasting. The selected currencies are Malaysian Ringgit (MYR) and Singapore Dollar (SGD). The proposed model was then evaluated by the Mean Absolute Percentage Error (MAPE) performance metric to test the robustness of the model. Lastly, a comparison between the proposed model and fuzzy time series model was conducted with respect to the MAPE. The results showed that the MAPE value for fuzzy time series-Markov chain was 0.9895% which fell under the criterion of highly accurate forecasting. Meanwhile, the MAPE value for fuzzy time series was 3.4306%. Thus, the forecasting performance of the proposed model was better than the fuzzy time series model. This study reveals the potential benefits of the proposed model as a highly accurate forecasting model.

A novel hybrid fuzzy time series model for prediction of COVID-19 infected cases and deaths in India

World is facing stress due to unpredicted pandemic of novel COVID-19. Daily growing magnitude of confirmed cases of COVID-19 put the whole world humanity at high risk and it has made a pressure on health professionals to get rid of it as soon as possible. So, it becomes necessary to predict the number of upcoming cases in future for the preparation of future plan-of-action and medical set-ups. The present manuscript proposed a hybrid fuzzy time series model for the prediction of upcoming COVID-19 infected cases and deaths in India by using modified fuzzy C-means clustering technique. Proposed model has two phases. In phase-I, modified fuzzy C-means clustering technique is used to form basic intervals with the help of clusters centroid while in phase-II, these intervals are upgraded to form sub-intervals. The proposed model is tested against available COVID-19 data for the measurement of its performance based on mean square error, root mean square error and average forecasting error rate. The novelty of the proposed model lies in the prediction of COVID-19 infected cases and deaths for next coming 31 days. Beside of this, estimation for the approximate number of isolation beds and ICU required has been carried out. The projection of the present model is to provide a base for the decision makers for making protection plan during COVID-19 pandemic.

Multivariate Markov Chain Model for Fuzzy Time Series

Multivariate Markov Chain Model for Fuzzy Time Series

Particle swarm optimization of partitions and fuzzy order for fuzzy time series forecasting of COVID-19

Major hyperparameters which affect fuzzy time series (FTS) forecasting are the number of partitions, length of partition intervals in the universe of discourse, and the fuzzy order. There are very few studies which have considered an integrated solution to optimize all the hyperparameters. In this paper, we strive to achieve optimum values of all three hyperparameters for fuzzy time series forecasting of the COVID-19 pandemic using the Particle Swarm Optimization (PSO) algorithm. We specifically propose two techniques, namely nested FTS-PSO and exhaustive search FTS-PSO for determining the optimal interval length, as an augmentation to the FTS-PSO model that optimizes the interval length and the fuzzy order. Nested PSO has two PSO loops: (i) the inner PSO optimizes the combination of fuzzy order and boundaries of intervals for a given number of partitions defined by the outer loop, and the resultant cost is fed back to the outer PSO; (ii) the outer PSO optimizes the number of partitions to reduce the cost while meeting the defined constraint. Exhaustive search FTS-PSO also has two loops where the inner loop is similar to nested FTS-PSO while the outer loop iterates over a pre-defined search space of number of partitions. We analyze the effectiveness of the two approaches by comparing with ARIMA, FbProphet, and the state-of-the-art FTS and FTS-PSO models. We adopt COVID-19 highly affected 10 countries worldwide to perform forecasting of coronavirus confirmed cases. We consider two phases of COVID-19 spread, one from the year 2020 and another from 2021. Our study provides an analytical aspect of the COVID-19 pandemic, and aims to achieve optimal number and length of intervals along with fuzzy order for FTS forecasting of COVID-19. The results prove that the exhaustive search FTS-PSO outperformed all the methods whereas nested FTS-PSO performed moderately well.

Air quality management using genetic algorithm based heuristic fuzzy time series model

PurposeThe purpose of this paper is to provide a better method for quality management to maintain an essential level of quality in different fields like product quality, service quality, air quality, etc.Design/methodology/approachIn this paper, a hybrid adaptive time-variant fuzzy time series (FTS) model with genetic algorithm (GA) has been applied to predict the air pollution index. Fuzzification of data is optimized by GAs. Heuristic value selection algorithm is used for selecting the window size. Two algorithms are proposed for forecasting. First algorithm is used in training phase to compute forecasted values according to the heuristic value selection algorithm. Thus, obtained sequence of heuristics is used for second algorithm in which forecasted values are selected with the help of defined rules.FindingsThe proposed model is able to predict AQI more accurately when an appropriate heuristic value is chosen for the FTS model. It is tested and evaluated on real time air pollution data of two popular tourism cities of India. In the experimental results, it is observed that the proposed model performs better than the existing models.Practical implicationsThe management and prediction of air quality have become essential in our day-to-day life because air quality affects not only the health of human beings but also the health of monuments. This research predicts the air quality index (AQI) of a place.Originality/valueThe proposed method is an improved version of the adaptive time-variant FTS model. Further, a nature-inspired algorithm has been integrated for the selection and optimization of fuzzy intervals.

A forecasting model for time series based on improvements from fuzzy clustering problem

This article proposes a new fuzzy time series model that can interpolate historical data, and forecast effectively for the future. It is combination of the improved steps from the existing models. There are problems to use the percentage variations of series between consecutive periods of time as a universal set, to divide the universal set into clusters by the automatic algorithm based on the similarity between elements, to determine the relationships between elements in the series and the divided clusters by the improved fuzzy cluster analysis algorithm, and to interpolate the historical data and to forecast for future by new principle. The proposed algorithm is performed quickly and efficiently by the established Matlab procedure. It is illustrated by an example, and tested for many other data sets, especially for 3003 series in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also apply the proposed model in forecasting the salty peak for a coastal province of Vietnam. Examples and application show the potential of the studied problem.

Dynamic panel fuzzy time series model and its application to econometric time series

This study proposes a new Fuzzy Time Series (FTS) approach, called as Dynamic Panel Fuzzy Time Series (DPFTS) which combines Dynamic Panel Data Analysis and FTS. The major advantages of proposed approach can be summarized as follows: i) proposed approach is adapted version of traditional fuzzy time series (TFTS) model to time series data having more than two cross-sections such as countries, cities, regions etc, in other words to panel data. Hence, it has the ability of globally determining the fuzzy sets and the fuzzy relations to be represent a large number of time series simultaneously, ii) it can construct FTS models even if time series have very small sample size since panel data are constructed by combining the time and cross-section dimensions. In order to evaluate the performance of proposed approach and compare it with its traditional version, two experiments which compose of a simulation study and a real time examples are conducted. Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) criteria are chosen for performance comparisons. Experimental results show that proposed approach exhibits considerable good performance in prediction and forecasting.

Fuzzy Time Series for Projecting School Enrolment in Malaysia

There are a variety of approaches to the problem of predicting educational enrolment. However, none of them can be used when the historical data are linguistic values. Fuzzy time series is an efficient and effective tool to deal with such problems. In this paper, the forecast of the enrolment of pre-primary, primary, secondary, and tertiary schools in Malaysia is carried out using fuzzy time series approaches. A fuzzy time series model is developed using historical dataset collected from the United Nations Educational, Scientific, and Cultural Organization (UNESCO) from the year 1981 to 2018. A complete procedure is proposed which includes: fuzzifying the historical dataset, developing a fuzzy time series model, and calculating and interpreting the outputs. The accuracy of the model are also examined to evaluate how good the developed forecasting model is. It is tested based on the value of the mean squared error (MSE), Mean Absolute Percent Error (MAPE) and Mean Absolute Deviation (MAD). The lower the value of error measure, the higher the accuracy of the model. The result shows that fuzzy time series model developed for primary school enrollments is the most accurate with the lowest error measure, with the MSE value being 0.38, MAPE 0.43 and MAD 0.43 respectively.

FQTSFM: A fuzzy-quantum time series forecasting model

The study shows that there are two main problems that affect the performance of fuzzy time series (FTS) models, namely the selection of the universe of discourse and the determination of the fuzzy degree of the memberships. However, the selection of the appropriate universe of discourse along with the degree of memberships is simultaneously associated with the multiobjective optimization problem (MOOP). Therefore, in this study, an improved version of the quantum optimization algorithm (QOA) has been proposed to find their optimal solutions. This improved QOA is called fast forward quantum optimization algorithm (FFQOA). Finally, by integrating FFQOA with the FTS modelling approach, a hybrid model called fuzzy-quantum time series forecasting model (FQTSFM) is designed. The main objective of FFQOA in FQTSFM is to select the Pareto-optimal front (POF) from all optimal non-dominated Pareto solutions by using the archive and grid concept during simulation. The main advantages of the proposed FQTSFM are that it converges very fast compared to the existing hybridized based FTS models and is able to evolve one-step ahead forecasted results. The FQTSFM is tested with three different datasets, namely daily average temperatures of Taipei, Taiwan Futures Exchange (TAIFEX) index and Taiwan Stock Exchange Corporation (TSEC) weighted index. The performance of the FQTSFM is compared with various established well-known FTS and non-FTS models in terms of different statistical metrics. In the case of daily average temperatures, TAIFEX index and TSEC weighted index datasets, the FQTSFM achieves correlation coefficients of 0.9988, 0.9978 and 0.9768, respectively. For daily average temperatures, TAIFEX index and TSEC weighted index datasets, the Theil’s U statistic values of the FQTSFM are 0.0022, 0.0022 and 0.0054, respectively. The FQTSFM has mean squared errors of 0.3959, 22.3965 and 83.6793 for the daily average temperatures, the TAIFEX index and the TSEC-weighted index datasets, respectively. In the case of daily average temperatures, TAIFEX index and TSEC weighted index datasets, the FQTSFM shows cross entropy values of 3.3498, 189.5018 and 708.0296, respectively. These metrics, including other empirical analyses, confirm that the forecasted accuracy of the proposed FQTSFM exceeds that of well-known time series models.

Financial Sequence Prediction Based on Swarm Intelligence Algorithms of Internet of Things

In order to accurately predict the financial time series and stock price fluctuation, in this study, metadata was used to ensure the objectivity of data for most of the swarm intelligence algorithms of the Internet of Things. The results show that the combination of theoretical methods and financial time series forecasting model can significantly improve the forecasting effect. At the same time, the proposed fuzzy theory also gives a totally different perspective to the modeling of financial time series which has stochastic and uncertain characteristics. Therefore, swarm intelligence algorithm and fuzzy theory are effectively combined, and their combination is very useful for the improvement of two financial fuzzy time series models. Because of their combination, the problem of stock price forecasting with different orders and different factors is well solved. Besides, it also provides two new solutions for such problems respectively as well as additional model choices for investors to avoid risks and improve returns.

Modeling the Nigerian Bonny Light Crude Oil Price: The Power of Fuzzy Time Series

Several authors have used different classical statistical models to fit the Nigerian Bonny Light crude oil price but the application of machine learning models and Fuzzy Time Series model on the crude oil price has been grossly understudied. Therefore, in this study, a classical statistical model—Autoregressive Integrated Moving Average (ARIMA), two machine learning models—Artificial Neural Network (ANN) and Random Forest (RF) and Fuzzy Time Series (FTS) Model were compared in modeling the Nigerian Bonny Light crude oil price data for the periods from January, 2006 to December, 2020. The monthly secondary data were collected from the Nigerian National Petroleum Corporation (NNPC) and Reuters website and divided into train (70%) and test (30%) sets. The train set was used in building the models and the models were validated using the test set. The performance measures used for the comparison include: The modified Diebold-Mariano test, the Root Mean Square Error (RMSE), the Mean Absolute Percentage Error (MAPE) and Nash-Sutcliffe Efficiency (NSE) values. Based on the performance measures, ANN (4, 1, 1) and RF performed better than ARIMA (1, 1, 0) model but FTS model using Chen’s algorithm outperformed every other model. The results recommend the use of FTS model for forecasting future values of the Nigerian Bonny Light Crude oil. However, a hybrid model of ARIMA-ANN or ARIMA-RF should be built and compared with Chen’s algorithm FTS model for the same data set to further verify the power of FTS model using Chen’s algorithm.

A Novel Stochastic Fuzzy Time Series Forecasting Model Based on a New Partition Method

Fuzzy Time Series (FTS) models are commonly used in time series forecasting, where they do not require any statistical assumptions on time series data. FTS models can handle data sets with a small number of observations or with uncertainty. This is a general advantage of FTS as compared with other techniques. However, FTS models still have some criticisms, such as the optimal lengths of intervals and the proper weights, which always influence the model accuracy and still have been of many concerns in literature. The work in this paper proposes a novel FTS forecasting model based on a new tree partitioning method (TPM) and Markov chain (MC), called FTSMC-TPM, for determining the optimal partitions of intervals and the proper weights vectors respectively, and this will greatly improve the model accuracy. The efficiency of the FTSMC-TPM model is tested using two types of time series consisting of the air pollution index (API) data, which is collected from Kuala Lumpur, Malaysia and the benchmark data of the yearly enrollments for the University of Alabama. Three statistical criteria have been used for investigating the accuracy of the proposed model. The results indicate that the proposed model outperforms the existing classic and advanced time series models in terms of forecasting accuracy. In addition, the proposed model shows the ability to successfully deal with forecasting problems to obtain higher model accuracy, which is examined in comparison with the existing models to validate its superiority. Hence, this study demonstrates that the proposed model is more suitable for the accurate prediction of air pollution events as well as for forecasting any type of random time series.

Heuristic hidden Markov model for fuzzy time series forecasting

This paper presents FTS forecasting model using hidden Markov model (HMM) and genetic algorithm (GA). Over the years, traditional methods such as Baum Welch algorithm (BWA) have been employed signi...

Heuristic hidden Markov model for fuzzy time series forecasting

Heuristic hidden Markov model for fuzzy time series forecasting

Application of fuzzy time series forecasting approach for predicting an enterprise net income level

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.

A novel probabilistic intuitionistic fuzzy set based model for high order fuzzy time series forecasting

The present research proposes a novel probabilistic intuitionistic fuzzy time series forecasting (PIFTSF) model using support vector machine (SVM) to address both uncertainty and non-determinism associated with real world time series data. In this model, the probability of membership values of crisp observation is determined to handle the statistical uncertainty. At the same time, the intuitionistic fuzzy element of crisp observation is determined to handle the non-statistical uncertainty along with non-determinism. Then, both the membership values are aggregated to obtain the probabilistic intuitionistic fuzzy element which handles both statistical and non-statistical uncertainty along with non-determinism due to hesitancy. Additionally, a novel trend-based discretization (TBD) method is proposed to determine the universe of discourse and number of intervals (NOIs) of fuzzy time series (FTS). For the first time, the fuzzy logical relationships (FLRs) are established for the probabilistic intuitionistic fuzzy set by considering the ratio trend variation (RTV) of crisp observation along with the mean of aggregated membership values which is modelled using SVM. The efficiency of the proposed PIFTSF model is demonstrated with sixteen diversified time series datasets and seven existing FTS models. A sensitivity analysis is carried out with respect to different design strategies to ensure the robustness of the proposed model. Extensive statistical analyses on obtained results confirm the superiority of the proposed model over other existing models. Further, Wilcoxon signed rank test, and Friedman and Nemenyi hypothesis test ensures the accuracy, robustness and reliability of the proposed model against its counterparts.

Fuzzy Estimations for Detecting Abrupt Changes: Cases on Tourism Series

This article deals with problems of detecting abrupt changes in time series ba Change Point Model (CPM) framework. We propose a fuzzification in a Fuzzy Time Series (FTS) model to eliminate a trend in a contaminated dependent series. The independent residuals are then inputed on the CPM method. In simulating an abrupt change, an ARIMA(1,1,1) and variance of the model are considered. The abrupt change is modelled as an AO (Additive Outlier) type of outliers. The minimum weight or breaksize of the abrupt change is defined based on the ARIMA variance formulated in this article. The percentage of uncorrelated residuals obtained by the FTS model and the percentage of correct detection of the proposed procedure are shown by simulation. The proposed detecting algorithm is implemented to detect abrupt changes in monthly tourism series in literature, i.e., in Taiwan and in Bali. The first series shows a slowly increasing trend with one abrupt change while the second series exhibits not only a slowly increasing trend but also a strong seasonal pattern with two abrupt changes. For comparison, we detect the changes in the empirical examples on an existing automatic detection procedure using tso package in R. For the first example, the results show that both detecting procedures give exactly a similar location of one change point where the package recognises it as an AO type of outliers. The abrupt change is related to the period of SARS outbreak in Taiwan. On the second example, the proposed procedure locates 4 change points which form two locations of changes, i.e., the first two change points are within 2 time points so do the last two change points. The locations are closed to times of Bali Bombing events. Meanwhile, the automatic procedure recognizes only one AO outlier on the series.

Annual Precipitation in Southern of Madagascar: Modeling using High Order Fuzzy Time Series

The objective of this research is to find the best conventional high order fuzzy time series model for annual precipitation series in southern Madagascar. This work consists on finding the hyper parameters (number of partition of the universe of discourse and model order) to obtain the best conventional high order fuzzy time series model for our experimental data. In previous works, entitled spatial and temporal variability of precipitation in southern Madagascar, we subdivided the study area between 22 ° S to 30 ° S latitude and 43 ° Eto 48 ° E longitude into four zones of homogeneous precipitation. In this article, we seek to model annual precipitation data representative of one of these four areas. These data were taken between 1979 and 2017. Our approach consists on subdividing the data: data obtained from 1979 to 2001 (60%) for the training and data from 2002 to 2017 (40%) to test the model. To determine the number of partitions and model order, we fix first the number of partitions to 10 and then to 15, 20, 25,30, 35, 40, 45 and 50.For each of these values, we vary the model order from 1 to 10.Thenwe locate the model order which corresponds to the minimum of the average curve between the Mean Absolute Errors (MAE) between the training data and the test data. Thus, the orders of the candidate model are 2, 3, 5, and 6.The next step is to fix the model order with the previous values and vary the number of partitions from 3 to 50.For each couple of hyper parameter of the model (number of partitions, model order), we locate the value of number of partitions corresponding to the minimum of the average curve between the absolute mean of the errors or MAE (Mean Absolute Error) between the train and test data. We obtain the hyper-parameter pairs (37, 2), (20, 3), (35, 5) and (35, 6).The first pair gives the lowest Mean Absolute Error. As a final result, we obtain the best high order fuzzy time series model with hyperparameters number of partition equals thirty seven and of order equals two for annual precipitation in Southern of Madagascar

Forecasting in non-stationary environments with fuzzy time series

Time series arise in many fields of science such as engineering, economy and agriculture to cite a few. In the early 1990’s the so called Fuzzy Time Series were proposed to handle vague and imprecise knowledge in time series data and have since become competitive forecasting models. A common limitation of recent fuzzy time series models is their inability to handle non-stationary data. Thus, in this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS). In the proposed method, we employ Non-Stationary Fuzzy Sets, in which perturbation functions are used to adapt the membership function parameters in the knowledge base in response to statistical changes in the time series. The flexibility of the method by means of computational experiments was tested with eight synthetic non-stationary time series data with several kinds of concept drifts, four real market indices (Dow Jones, NASDAQ, SP500 and TAIEX), three real FOREX pairs (EUR-USD, EUR-GBP, GBP-USD), and two real cryptocoins exchange rates (Bitcoin-USD and Ethereum-USD). As competitor models the Time Variant fuzzy time series and the Incremental Ensemble were used, these are two of the major approaches for handling non-stationary data sets. The proposed method shows resilience to concept drift, by adapting parameters of the model, while preserving the symbolic structure of the knowledge base.

New hybrid fuzzy time series model: Forecasting the foreign exchange market

<span class="fontstyle0">This paper develops the comparison of the volatility prediction of the traditional<br />models (ARIMA, EGARCH, and PARCH), with respect to the Hybrid Fuzzy Time<br />Series and Fuzzy ARIMA Model of Tseng’s and Tanaka’s methodology (FTS-Fuzzy<br />ARIMA Tseng and FTS-Fuzzy ARIMA Tanaka). For this purpose, it applies to the<br />time series of the foreign exchange market to forecast the foreign currency exchange rate of Mexican Pesos against American Dollar, the growth rate of the time series data in a daily format from January 2008 to December 2017, to perform the sample test is used January 2018. The main result is that the models based on fuzzy theory generate a better estimate of the volatility of the foreign exchange rate.</span> <br /><br />