Application of Fuzzy Time Series Method Cheng Model in Forecasting Stock Prices PT Bukit Asam Tbk

Investment in stocks is one type of investment that can get huge profits, but there are also great risks. So it is necessary to analyze in advance before starting an investment in stocks, in order to avoid losses. One way is to forecast the stock price using fuzzy time series Cheng. The data used is weekly period stock price data from PTBA in January 2020 - December 2022, which can be categorized as a form of time series. From this research, the forecasting value for the next period is Rp. 3797. Which results in a MAPE of 4.2%, which means that FTS Cheng method is very good to use in forecasting the share price of PT Bukit Asam Tbk, because it produces a MAPE value <10%, and produces an RMSE of 158 rupiah, which means the average of the difference between actual and forecast values .


Introduction
Stock investment is one type of investment that can generate a lot of profit, but investing in stocks can also provide big losses too.So that an analysis must be carried out before starting to invest in stocks.One way to analyze it is by forecasting the stock price [1].There are several forecasting methods, such assuch as Fuzzy Time Series (FTS), ARCH-GARCH model, Exponential Smoothing, Box-Jenkins, and Moving Average.In this study I chose FTS because stock price data is time series data, which requires historical data to process FTS [2].The advantage of the fuzzy time series method is that it can determine the characteristics of the actual data, and can find a pattern which will then be used for stock price forecasting [3].In the FTS process, it also does not require anything learning systems from complex systems, such as artificial neural networks or genetic algorithms, so that they can be processed or processed and developed more easily [4].
Fuzzy logic is a component of soft computing, which has been widely applied in various fields.One of its applications is to help humans in making a decision.In this study, fuzzy logic will be used to analyze stock price time series data, which will be formed into a forecasting model.Fuzzy logic is used in stock price forecasting because fuzzy set theory can provide an appropriate and precise theoretical framework in calculating data patterns, and can produce tolerance for uncertainty [5].
Several studies have used the FTS method, including [6] in this study FTS was used to predict PT Telkom Indonesia's share price in January -December 2017.The forecasting results have good criteria, because it produces a MAPE of 0.57.In research [7] used the FTS Cheng model to predict an increase in the number of BPJS participants who receive APBN contributions.From this research obtained an increase in BPJS participants who received APBN contribution assistance in 2019-2021 by 52,071 participants.Forecasting in this study has very good criteria, because it produces a MAPE value of <10%.Which produces a MAPE of 0.97%, which means the forecasting accuracy in this study is 99.03% [8].
This study uses the FTS Cheng method to forecast PTBA's share price, using data for the period January 2020 to December 2022.

Forecasting.
Forecasting is one of the sciences that discusses predicting what might happen in the future.Because, forecasting requires historical data which will then be projected in the future using a mathematical model.

Time Series
A time series or time series is a collection of data that represents the behavior of one or more random variables over time, and its main characteristics are that each variable in a time series is not independent of one another, and analysis of time series must consider the order of the data to be observed [7]

Fuzzy Time Series Cheng
The FTS Cheng method has a slightly different processing step compared to other FTS, which is in determining the interval, namely using FLR (Fuzzy Logical Relationship) by entering all relationships and giving weights based on the sequence and repetition of the same FLR [9].
Processing steps using Cheng's fuzzy time series method can be seen as follows [10] Where   ( = 1,2,3, … , ) is part of the universe set and the number given the symbol " " means that the degree of the member to the value   ( = 1,2,3, … , )where the value is 1 or 0.5 or 0.

Fuzification
Fuzzification is the initial process of a system that uses fuzzy logic, which is a way of converting membership data from ordinary (conventional) sets into membership fuzzy sets.

Form a fuzzy logical relationship (FLR)
Determines the FLR view of the actual data according to time.FLR is denoted by   →   , which   is called the current state or LH (Left Hand) and   is called the next state or RH (Right Hand).The current state value is obtained from the actual data fuzzification result ( − 1) and the next state value is obtained from the actual data fuzzification result ().6. Define fuzzy logical relationship group (FLRG) In determining the FLRG weights, it is done by including all the relationships from the FLR and giving weights by looking at the same sequence and repetition.FLRs that have the same Left Hand () will be grouped together  ( = 1)  2 →  2 , is given a weight of 1

Defuzzification
To determine the forecast value, the matrix  * is multiplied by the middle value (  ), so that the forecast calculation is obtained as follows: is the result of forecasting.
If the result of fuzzification at time- is   , which   does not have FLR at condition   → ∅, and also the maximum value of the degree of its members is at   , then the value   is the middle value of   , which is denoted by   [16]- [21].

Forecasting Accuracy
Generally, the accuracy of a forecasting result is calculated by comparing actual data and research data, to determine the accuracy of the research results and the errors (errors) obtained from the forecasting.In this study, MAPE and RMSE indicators were used to determine the accuracy of the forecasting which   is the actual value in the -period,   is the forecasted value in the-th period, and  is the amount of data.
Forecasting criteria based on MAPE values [22], are as follows:

Research Methods
The data to be used in this study is secondary data, in which the data is taken from existing sources.The data to be processed is stock price data with a weekly period, from January 2020 to December 2022.Stock price data is time series data, so the Fuzzy Time Series Cheng method will be used in this study.The data will then be applied using the fuzzy time series method.Next, calculate the accuracy of the forecasting results using the Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) indicators.Then several forecasting experiments were carried out on the historical data of PT Bukit Asam Tbk stock prices with different time periods and amounts of data, using the help of a program that had previously been created by the researcher https://apiptba.alyanadhira.repl.co/.The next step is to draw conclusions and suggestions obtained after conducting this research [23][24] [25], [26].

Results and Discussion
The data used is weekly stock price data from PT Bukit Asam Tbk from January 2020 to December 2022 in rupiah units (Rp).The data is obtained from the Investing.comwebsite (https://www.investing.com/equities/tb-bukit-asamhistorical-data).

Conclusion
PTBA's stock price forecasting using FTS Cheng has very good criteria, because it produces a MAPE value of less than 10%, namely 4.2%.The average difference from actual and forecast data is 158 rupiah.
After several forecasting experiments, it was found that when the stock price movement pattern tends to be stable or the price movement pattern is not too extreme, forecasting using FTS Cheng will be more accurate, because it will produce a smaller MAPE value.Then it was found that, by conducting experiments with a larger amount of data does not have implications for the accuracy of forecasting results on stock prices.

Suggestion
From the research results of stock price forecasting using the method that has been done, this research can only predict one period ahead.So it is suggested for further research to use different observation data or use different forecasting methods.Which can produce forecast values in more periods and which can produce forecast values that are more varied, such as the Artificial Neural Network (ANN) method, Adaptive Neuro Fuzzy Inference System (ANFIS), or can use other fuzzy time series methods.So it is hoped that the results of this study can be used as material for consideration or reference to expand research on FTS Cheng for further research.

Figure
Figure 1.actual data ), which   is the matrix weight in the i-th row and j-th column, each of which corresponds to the left hand (  ) and right hand (  ).So that the matrix can be written as follows: * = (  * ), ,  = 1,2, … , , which   * () is done with the following formulation:

experiment uses a program that has been created by the researcher 1
From this graph, the lowest price for PT Bukit Asam Tbk shares is Rp.1,800 and the highest price is Rp.4,630,-The actual data processing steps for PT Bukit Asam Tbk's share price using the fuzzy time series method are as follows:1.Finding the universal set ()Based on actual data the smallest data (  ) is obtained which is 1800 and the largest data (  ) is 4630.Then it  1 and  2 is given a value of 0 and 14.So that the universe set is obtained based on equation (1.out based on previously obtained class intervals, on actual data that has been converted into linguistic numbers.Determining the fuzzification value is done by defining the actual data into the appropriate class intervals.Fuzzy relations can be formed from  − 1 data to  data fuzzification results, which can be written as  −1 →   .From the FLRG it can be seen the weighting value.As an example, current state  1 own next state  1 and  2 .So that we get weights  1 →  1 there are as many as 36 and  1 →  2 the weight value are 5. stock price forecasting produces a MAPE value of 4.2%, because the MAPE value is <10%, the forecast using FTS Cheng has very good criteria.On this fortune-telling also earnthe average error or difference from actual and forecast data is 158 rupiah. .First try Using PT Bukit Asam Tbk stock price data for the period January 2018 to March 2023.