Implementation of digital fuzzy time series Markov chain in price forecasting and investment risk analysis with value at risk

Rainfall is essential in many areas of life, including agriculture, water resource management, and disaster mitigation. Padang Panjang is one of the cities with high rainfall. Rainfall varies throughout the year, affecting agriculture and people's livelihoods. Therefore, accurate rainfall estimation is required to support effective planning and management. This study aims to forecast the amount of rainfall in Padang Panjang City from January 2020 to November 2024 using the fuzzy time series method of the Cheng model. The data is on the monthly rainfall amount from January 2020 to November 2024, obtained from the BMKG Padang Pariaman Climatology Station. The stages in the fuzzy time series Cheng model are forming the universe set, forming intervals, fuzzifying the data, analyzing Fuzzy Logical Relationship (FLR) and Fuzzy Logical Relationship Group (FLRG), determining the weight of the relationship, forecasting, and measuring the accuracy of predicting using Mean Absolute Percentage Error (MAPE). The forecasting results were validated using MAPE, with a value of 41%, which indicates that the model is feasible. The forecasting results for the following three periods are December 2024 high rainfall, January 2025 medium rainfall, and February 2025 high rainfall. This research shows that the fuzzy time series method of the Cheng model can be used as an alternative means of forecasting time series data.

Unemployment is a significant socio-economic problem in Lhokseumawe City that requires serious attention from policymakers. The unemployment rate fluctuates from year to year, making accurate forecasting an important aspect in formulating effective strategies and policies to reduce unemployment. One method that can be used to analyze and forecast time series data with uncertainty is the Fuzzy Time Series (FTS) method, which applies fuzzy logic concepts to handle vague and imprecise data patterns. In this study, the Fuzzy Time Series method is applied to predict the number of unemployed people in Lhokseumawe City. The data used are historical unemployment data over a period of 10 years, from 2013 to 2022. The research process begins with defining the universe of discourse (U), determining the number and length of interval classes, defining fuzzy sets on U, and fuzzifying the unemployment data. Furthermore, Fuzzy Logical Relationships (FLR) are identified and grouped into Fuzzy Logical Relationship Groups (FLRG). The defuzzification process is then carried out to obtain crisp values, followed by forecasting calculations.The analysis was conducted using the RStudio application. The forecasting results show that the predicted number of unemployed people in 2023 is 10,514.125, which is rounded to 10,514 people. The accuracy of the forecasting model is evaluated using Mean Absolute Percentage Error (MAPE) and Average Forecasting Error Rate (AFER), both of which yield values of 6.70%. Since the MAPE and AFER values are less than 10%, the forecasting results can be categorized as very good and reliable for decision-making purposes.

Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures

In this paper, we present a new method to forecast the daily Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series and fuzzy variation groups, where the main input factor is the previous day's TAIEX, and the secondary factor is either the Dow Jones, the NASDAQ, the M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1b</sub> , or their combination. First, the proposed method fuzzifies the historical training data of the TAIEX into fuzzy sets to form fuzzy logical relationships. Second, it groups the fuzzy logical relationships into fuzzy logical relationship groups (FLRGs) based on the fuzzy variations of the secondary factor. Third, it evaluates the leverage of the fuzzy variations between the main factor and the secondary factor to construct fuzzy variation groups. Fourth, it gets the statistics of the fuzzy variations appearing in each fuzzy variation group. Fifth, it calculates the weights of the statistics of the fuzzy variations appearing in each fuzzy variation group, respectively. Finally, based on the weights of the statistics of the fuzzy variations appearing in the fuzzy variation groups and the FLRGs, it performs the forecasting of the daily TAIEX. Because the proposed method uses both fuzzy variation groups and FLRGs to analyze in detail the historical training data, it gets higher forecasting accuracy rates to forecast the TAIEX than the existing methods.

This research aims to apply the Fuzzy Time Series Markov Chain combined with Kernel Smoothing in forecasting stock prices. The Kernel Smoothing technique is used to smooth stock data before the fuzzification process, resulting in more accurate predictions. The research stages include Data Smoothing, Fuzzy interval formation, Fuzzy Logical Relationship and Fuzzy Logical Relationship Group formation, and forecasting using Markov Chain Transition Matrix. Evaluation using MAPE shows a low prediction error rate, with a value of 0.005974257%, so this method is effective for volatile stock data. The implementation of this model is expected to be a reference for investors and analysts in understanding and predicting future stock price movements.

The study of fuzzy time series models have been extensively used to improve the accuracy rates in forecasting problems. In this paper, we present a new type 2 fuzzy time series forecasting model based on three-factors fuzzy logical relationship groups. The proposed method uses a new technique to define partitions the universe of discourse into different length of intervals for different factors. Also, the proposed method fuzzifies the historical data sets of the main factors, second factors and third factors to their maximum membership grades obtained by their corresponding triangular fuzzy sets and construct the fuzzy logical relationship groups which is based on the three-factors to enhance in the forecasting accuracy rates. This paper introduces a new defuzzification technique based on their frequency occurrences of fuzzy logical relationships in fuzzy logical relationship groups. The fitness of the propose method is verified in the forecasting of Bombay Stock Exchange (BSE) Sensex historical data and compare in terms of root mean square and average forecasting errors which indicates that the proposed method produce more accurate forecasted output over the existing models in fuzzy time series.

Fuzzy logic relationship groups are crucial to fuzzy time series prediction. In generally, fuzzy logic relationship groups can be constructed by manually mining fuzzy logic relationship between adjacent data in time series. However, for the large-scale or long-term time series, the way of manually constructing fuzzy logical relationship groups is difficult and infeasible. In this paper, a hybrids prediction algorithm based on Fuzzy Cognitive Map (FCM) is proposed, in which fuzzy c-means clustering algorithm is used to construct the framework of FCM and genetic algorithm (GA) is applied to learn weights of FCM. Finally, a fully learned fuzzy cognitive map is used to represent, store fuzzy logic relationships of fuzzy time series and realize prediction. A benchmark time series — the enrollments of University of Alberta time series is applied to validate the feasibility and effectiveness of the proposed algorithm, whose results show that the proposed prediction algorithm based on FCM is effective and can obtain the satisfactory prediction precision. It is a potential virtue that the proposed algorithm can automatically process the prediction problem of the large-scale or long-term time series.

Deep learning methods have excellent prospects for application in wave forecasting research. This study employed the convolutional LSTM (ConvLSTM) algorithm to predict the South China Sea (SCS) significant wave height (SWH). Three prediction models were established to investigate the influences of setting different parameters and using multiple training data on the forecasting effects. Compared with the SWH data from the China–France Ocean Satellite (CFOSAT), the SWH of WAVEWATCH III (WWIII) from the pacific islands ocean observing system are accurate enough to be used as training data for the ConvLSTM-based SWH prediction model. Model A was preliminarily established by only using the SWH from WWIII as the training data, and 20 sensitivity experiments were carried out to investigate the influences of different parameter settings on the forecasting effect of Model A. The experimental results showed that Model A has the best forecasting effect when using three years of training data and three hourly input data. With the same parameter settings as the best prediction performance Model A, Model B and C were also established by using more different training data. Model B used the wind shear velocity and SWH as training and input data. When making a 24-h SWH forecast, compared with Model A, the root mean square error (RMSE) of Model B is decreased by 17.6%, the correlation coefficient (CC) is increased by 2.90%, and the mean absolute percentage error (MAPE) is reduced by 12.2%. Model C used the SWH, wind shear velocity, wind and wave direction as training and input data. When making a 24-h SWH forecast, compared with Model A, the RMSE of Model C decreased by 19.0%, the CC increased by 2.65%, and the MAPE decreased by 14.8%. As the performance of the ConvLSTM-based prediction model mainly rely on the SWH training data. All the ConvLSTM-based prediction models show a greater RMSE in the nearshore area than that in the deep area of SCS and also show a greater RMSE during the period of typhoon transit than that without typhoon. Considering the wind shear velocity, wind, and wave direction also used as training data will improve the performance of SWH prediction.

Each investment object being traded in the stock market will get return that it has risk potential. Return and risk has mutual correlation that equilibrium. If the risk is high, then it obtains high return and vice versa. Risk management is the desain and implementation procedure for controlling risk. Value at Risk (VaR) is instrument to analyze risk management. Financial time series data for return data is assumed that it has heavy tail distribution and heteroscedasticity case (volatility clustering). Time series model that used to modelling this condition are Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregresive Conditional Heteroscedasticity (GARCH), while Value at Risk calculation is used Generalized Pareto Distribution (GPD) approach. This research uses return data from stock closing prices of Kimia Farma Pusat period October 2009 until September 2014. The best ARCH-GARCH model is ARIMA(0,1,1) GARCH(1,2) model because the parameters are significant and it has the smallest AIC value. Risk calculation that is gotten with GPD approach if invest in Kimia Farma Pusat with interval confidence 95% is 13.6928% rupiah from current asset. Keywords : Stock, Risk, Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Generalized Pareto Distribution (GPD), Value at Risk (VaR)

This study aims to analyze fluctuations in Indonesian gold prices using the fuzzy time series Markov chain model. The Indonesian gold price will apply the fuzzy time series Markov chain model method by determining the universe and interval limits. Then from the gold price data, fuzzification and Determination of Fuzzy Logic Relations (FLR) are carried out. After that, the Fuzzy Logical Relationship Group (FLRG) was formed. Based on the FLRG, the initial forecast is then carried out. To obtain the final forecast, adjustments are made. The final forecasting result is obtained from the sum of the initial forecast results with the adjustment value. After the forecast is obtained, the level of goodness of the model is calculated using MSE, MAPE, and RMSE. Based on the results of the analysis and discussion carried out, the conclusion obtained is that the fuzzy time series Markov chain model method has a relatively good forecasting performance. This is indicated by the MAPE value &lt; 10% with MAPE validation of 0.936463%, and the fuzzy time series Markov chain model method can still produce good forecasts despite the new data.

Value at risk (VaR) and conditional value at risk (CVaR) are frequently used as risk measures in risk management. VaR estimates the maximum expected loss over a given time period at a given acceptance level, whereas CVaR measures the extreme risk or the risk beyond VaR. This paper aims to perform an empirical study on VaR and CVaR based on the daily returns of the Malaysian stock markets traded in Kuala Lumpur Composite Index (KLCI) over a time period using the RiskMetrics and the peaks over the threshold (POT) methods. In particular, the IGARCH (1, 1) model is applied for the RiskMetrics method, whereas the generalized Pareto distribution (GPD), a distribution based on an extreme value theory, is considered for the POT method. The results show that the GPD, which is considered in the POT method, provides an adequate fit to the data of threshold excesses, and the POT is a more reliable measure of risks compared to the RiskMetrics. Key words: Value at risk, conditional value at risk, RiskMetrics, peaks the over threshold, IGARCH, generalized Pareto.

In this paper, we present a new method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy time series, where the main factor is the TAIEX and the secondary factors are either the Dow Jones, the NASDAQ, the M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1b</sub> (Taiwan), or their combinations. First, we fuzzify the historical data of the main factor into fuzzy sets with a fixed length of intervals to form fuzzy logical relationships. Then, we group the fuzzy logical relationships into fuzzy logical relationship groups. Then, we evaluate the leverage of fuzzy variations between the main factor and the secondary factor to forecast the TAIEX. The experimental results show that the proposed method gets a higher average forecasting accuracy rate than Chen's method [1] and Huarng et al.'s method [9] to forecast the TAIEX.

The potential for stock market growth in Asian Pacific countries has attracted foreign investors. However, higher growth rates come with higher risk. We apply value at risk (VaR) analysis to measure and analyze stock market index risks in Asian Pacific countries, exposing and detailing both the unique risks and system risks embedded in those markets. To implement the VaR measure, it is necessary to perform "volatility modeling" by mixture switch, exponentially weighted moving average (EWMA), or generalized autoregressive conditional heteroskedasticity (GARCH) models. After estimating the volatility parameters, we can calibrate the VaR values of individual and system risks. Empirically, we find that, on average, Indonesia and Korea exhibit the highest VaRs and VaR sensitivity, and currently, Australia exhibits relatively low values. Taiwan is liable to be in high-state volatility. In addition, the Kupiec test indicates that the mixture switch VaR is superior to delta normal VaR; the quadratic probability score (QPS) shows that the EWMA is inclined to underestimate the VaR for a single series, and GARCH shows no difference from GARCH t and GARCH generalized error distribution (GED) for a multivariate VaR estimate with more assets.

&lt;span lang="EN-US"&gt;Accurate predictions of national rice production are crucial for food sustainability, yet data fluctuations pose a major challenge. This study aims to improve forecasting accuracy by developing a modified Fuzzy Time Series (FTS) model that simplifies the Fuzzy Logical Relationship Group (FLRG) by retaining only the logical relationships with the highest frequency of occurrence. Monthly Indonesian rice production data from January 2018 to March 2025 were used to test this model. To assess the effectiveness of this modification, the model’s performance was compared with Chen’s conventional FTS models of orders 1 to 3 through MAD, RMSE, and MAPE. Results indicate that the modified third-order FLRG achieved the best accuracy (MAD = 196,410; RMSE = 271,774; MAPE = 5.46%), while reducing FLRG complexity by 10.84%. This demonstrates that FLRG simplification effectively captures longer seasonal dependencies while reducing computational complexity. Nevertheless, the model’s sensitivity to sudden structural changes underscores the need for adaptive or probabilistic FLRG enhancement, with hybrid mechanisms as a potential complement. Overall, the proposed approach provides an efficient decision-support tool for maintaining food supply stability and guiding data-driven agricultural policy in Indonesia. &lt;/span&gt;

The novel coronavirus has played a disastrous role in many countries&#13;\nworldwide. The outbreak became a major epidemic, engulfing the entire world&#13;\nin lockdown and it is now speculated that its economic impact might be worse&#13;\nthan economic deceleration and decline. This paper identifies two different&#13;\nmodels to capture the trend of closing stock prices in Brazil (BVSP), Russia&#13;\n(IMOEX.ME), India (BSESN), and China (SSE), i.e., (BRIC) countries. We&#13;\npredict the stock prices for three daily time periods, so appropriate preparations can be undertaken to solve these issues. First, we compared the ARIMA,&#13;\nSutteARIMA and Holt-Winters (H-W) methods to determine the most effective model for predicting data. The stock closing price of BRIC country data&#13;\nwas obtained from Yahoo Finance. That data dates from 01 November 2019&#13;\nto 11 December 2020, then divided into two categories–training data and test&#13;\ndata. Training data covers 01 November 2019 to 02 December 2020. Seven&#13;\ndays (03 December 2020 to 11 December 2020) of data was tested to determine&#13;\nthe accuracy of the models using training data as a reference. To measure&#13;\nthe accuracy of the models, we obtained the means absolute percentage error&#13;\n(MAPE) and mean square error (MSE). Prediction model Holt-Winters was&#13;\nfound to be the most suitable for forecasting the Brazil stock price (BVSP)&#13;\nwhile MAPE (0.50) and MSE (579272.65) with Holt-Winters (smaller than&#13;\nARIMA and SutteARIMA), model SutteARIMA was found most appropriate to predict the stock prices of Russia (IMOEX.ME), India (BSESN), and&#13;\nChina (SSE) when compared to ARIMA and Holt-Winters. MAPE and MSE&#13;\nwith SutteARIMA: Russia (MAPE:0.7; MSE:940.20), India (MAPE:0.90;&#13;\nMSE:207271.16), and China (MAPE: 0.72; MSE: 786.28). Finally, HoltWinters predicted the daily forecast values for the Brazil stock price (BVSP)&#13;\n(12 December to 14 December 2020 i.e., 115757.6, 116150.9 and 116544.1),&#13;\nwhile SutteARIMA predicted the daily forecast values of Russia stock prices&#13;\n(IMOEX.ME) (12 December to 14 December 2020 i.e., 3238.06, 3241.54 and&#13;\n3245.01), India stock price (BSESN) (12 December to 14 December 2020 i.e.,.&#13;\n45709.38, 45828.71 and 45948.05), and China stock price (SSE) (11 December