Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
RESEARCH ARTICLE Implementation of Support Vector Regression (SVR) and Double Exponential Smoothing (DES) for Forecasting BRI Stock Prices Sitti Masyitah Meliyana*.
Muhammad Kasim Aidid .
Amaliyah Rahmadhani Statistics Department.
Mathematics and Natural Sciences Faculty.
Universitas Negeri Makassar.
Makassar.
Indonesia.
Abstract: This study aims to forecast the closing stock prices of BRI using *Corresponding author: Sitti Masyitah Meliyana.
Statistics Department.
Mathematics and Natural Sciences Faculty.
Universitas Negeri Makassar.
Makassar.
Indonesia E-mail: sittimasyitahmr@unm.
Support Vector Regression (SVR) and Double Exponential Smoothing (DES) The data used in this research is secondary data obtained from the Yahoo Finance website, covering the period from January 2020 to November The analytical steps using the SVR method involve selecting the optimal model by applying Grid Search Optimization to various kernels .
inear, polynomial, radial, and sigmoi.
The best-performing model was found to be the radial kernel with parameters A = 0.
C = 100, and = 10, yielding a Mean Absolute Percentage Error (MAPE) of 0.
2431%, which was then used for For the DES method, the steps involved parameter determination and minimizing the MAPE value, followed by smoothing calculations and The optimal parameters obtained were = 0.
89 and = 0.
resulting in a MAPE value of 1.
Based on the comparison of MAPE values, it can be concluded that the SVR method with a radial kernel (A = 0.
C = 100, = .
provides the most accurate forecasts for BRI closing stock prices, with the lowest MAPE of 0.
Keywords: Stock Price.
Support Vector Regression (SVR).
Double Exponential Smoothing (DES).
Mean Absolute Percentage Error (MAPE) Introduction The stock market is one of the sectors that plays an important role in a countryAos economy as it reflects both corporate performance and overall economic conditions.
The fluctuating movement of stock prices presents a challenge for investors in making the right investment Therefore, stock price forecasting becomes a crucial aspect of capital market analysis to reduce risks and increase profit potential.
Bank Rakyat Indonesia (BRI) is one of the largest banks in Indonesia, with a high market capitalization and significant stock price movements.
Since the COVID-19 pandemic.
BRIAos stock price has experienced sharp fluctuations, indicating uncertainty in the capital market.
Based on historical data.
BRIAos stock price experienced a significant decline in 2020 due to the pandemic, followed by a gradual recovery in the following years.
This phenomenon highlights the importance of stock price forecasting to help investors make more informed In recent years, various methods have been developed for stock price forecasting.
Traditional methods such as Autoregressive Integrated Moving Average (ARIMA) are often used, but they have limitations in capturing nonlinear patterns in time series data.
Therefore, more This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
advanced approaches such as Support Vector Regression (SVR) and Double Exponential Smoothing (DES) have begun to be applied in stock price forecasting analysis.
SVR, as a machine learning technique, can handle complex data patterns by detecting nonlinear relationships within the dataset.
Meanwhile, the DES method is known for its doublesmoothing approach that considers trends in historical data to improve forecasting accuracy.
Several previous studies have discussed the application of SVR and DES in stock price For example.
Rais et al.
demonstrated that SVR with a radial basis function (RBF) kernel outperformed conventional regression methods in forecasting inflation.
addition, a study by Syahfitri et al.
revealed that the use of SVR with Grid Search optimization improved accuracy in predicting gold prices.
On the other hand, research by Indriyani et al.
showed that the DES method produced good forecasting results on Bank Tabungan Negara (BTN) stock data, with a low MAPE value.
Although these studies show promising results, there is a research gap regarding the comparison of SVR and DES effectiveness in forecasting the stock prices of banking companies in Indonesia, particularly BRI.
Most studies only examine one method without conducting a direct comparison.
Therefore, this study aims to fill this gap by comparing the forecasting accuracy of BRIAos stock prices using both methods and determining which method is superior based on the Mean Absolute Percentage Error (MAPE) value.
Based on the background and gap analysis described above, the main objectives of this research are: To forecast BRI stock prices using the Support Vector Regression (SVR) method with Grid Search optimization to determine the best parameters.
To forecast BRI stock prices using the Double Exponential Smoothing (DES) method with smoothing parameter optimization.
To compare the forecasting accuracy of the two methods based on MAPE values and determine the more optimal method for forecasting BRI stock prices.
The importance of stocks as an investment instrument lies in their potential to generate income, reduce high costs, enhance investment capacity, and improve overall welfare.
Stocks serve as an investment tool that helps investors mitigate financial risks, which may occur if the stock price falls below its purchase price.
In this regard, forecasting stock price movements is essential to assist investors in determining the right timing for transactions.
forecast stock prices, statistical methods are required.
Hence, this study employs SVR and DES methods to forecast stock prices.
Literature Review Stock Price Forecasting Stock price forecasting is a process of predicting future price movements based on historical Forecasting approaches can be categorized into classical statistical methods, such as ARIMA, and machine learning-based methods, such as SVR.
While ARIMA has been widely applied in time series analysis, it has limitations in capturing complex and nonlinear patterns (Hyndman & Athanasopoulos, 2.
Consequently, machine learning approaches have gained increasing attention to overcome these shortcomings.
Support Vector Regression (SVR) Support Vector Regression (SVR) is a machine learning technique derived from Support Vector Machines (SVM), designed for regression tasks.
SVR aims to construct an optimal hyperplane that predicts target values within a specified error tolerance (Smola & Schylkopf.
Previous studies have demonstrated its effectiveness.
Rais et al.
found that SVR with a radial basis function (RBF) kernel achieved higher accuracy than linear regression in predicting stock prices, while Syahfitri et al.
highlighted the benefits of Grid Search optimization in enhancing SVR performance.
The general regression function of SVR can be expressed as:
This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
= yc ycN yuc.
where w denotes the weight vector, yuc.
the feature mapping, yca the bias, and yce.
the regression function.
The optimization process introduces slack variables yuO and yuOO to allow deviations, with a penalty parameter ya controlling the trade-off between margin maximization and prediction error (Smola & Schylkopf, 2.
Kernel functions commonly employed in SVR include linear, polynomial, sigmoid, and RBF (Yu et al.
, 2.
Grid Search Optimization Grid Search is a parameter optimization technique that systematically evaluates predefined parameter combinations to identify the most accurate model.
Cross-validation, particularly kfold cross-validation, is often used in conjunction with Grid Search to reduce overfitting and provide reliable error estimation (Santosa, 2007.
Han et al.
, 2.
Double Exponential Smoothing (DES) Double Exponential Smoothing (DES), introduced by Holt in 1958, is a forecasting method that applies double smoothing to account for level and trend components (Hudiyanti et al.
Unlike seasonal models.
DES focuses on trend-based forecasting by incorporating two parameters: yu .
evel smoothin.
and yu .
rend smoothin.
The model is defined as follows (Rosadi, 2.
ycIyc = yuycUyc .
Oe y.
cIycOe1 ycNycOe1 ) ycNyc = yu.
cIyc Oe ycIycOe1 ) .
Oe y.
ycNycOe1 yayc yco = ycIyc ycoycNyc .
where ycUyc is the actual observation, ycIyc the level, ycNyc the trend, and yayc yco the forecast for yco future periods.
Double Exponential Smoothing (DES) The Mean Absolute Percentage Error (MAPE) is a widely used metric for evaluating forecasting accuracy, defined as (Gurianto et al.
, 2.
Ocycuyc=1 ycAyaycEya = .
cUyc Oe yayc | ycUyc y 100% ycu .
where ycUyc is the actual value, yayc the forecast value, and ycu the number of observations.
A lower MAPE indicates higher accuracy.
Forecasting performance is categorized as very good if MAPE O 10%, good if 10% < MAPE O 20%, acceptable if 20% < MAPE O 50%, and poor if MAPE > 50% (Ferima Talia et al.
, 2.
Research Method The data used in this study consist of historical daily closing prices of BRI stocks from January 2020 to November 2023.
The variable employed is the daily closing stock price, which represents the final price or benchmark price of a stock in a single trading day.
Stock closing prices are measured in rupiah per share.
The data analysis techniques applied in this study are as follows:
Data collection: Secondary data on daily closing stock prices from January 2020 to November 2023, obtained from Yahoo Finance.
Plotting time series data.
Steps of analysis using Support Vector Regression (SVR):
This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
Determining the values of parameters C .
A .
, and .
using Grid Search Optimization.
Identifying the best model by evaluating the smallest parameter values across different kernels.
Conducting forecasting using the best-selected model.
Evaluating the forecasting accuracy using the Mean Absolute Percentage Error (MAPE).
Steps of analysis using Double Exponential Smoothing (DES):
Determining the optimal values of .
using the trial-and-error .
Selecting the smoothing parameters based on the smallest MAPE value.
Conducting forecasting using the best smoothing parameters.
Selecting the best method by comparing the MAPE values of both models.
Drawing conclusions based on the results of the analysis.
Results and Discussion Descriptive Analysis The descriptive analysis of the daily closing prices of BRI stocks from January 2020 to November 2023 is presented in Table 1.
Table 1: Descriptive Analysis of BRI Stock Closing Prices (IDR) Mean
3,683
Minimum
1,655
Maximum
5,410
As shown in Table 1, the average closing price of BRI stocks during the period from January 1, 2020, to November 30, 2023, was IDR 3,683 per share.
The lowest closing price was IDR 1,655 per share, recorded on May 18, 2020, while the highest closing price was IDR 5,410 per share, recorded on August 10, 2023.
The plot of BRIAos daily closing stock prices over the period January 2020 to November 2023 is presented in Figure 1.
Figure 1: Plot of Daily Closing Stock Prices.
January 2020 Ae November 2023 Based on Figure 1, the daily closing prices of BRI stocks from 2020 to 2023 exhibit a trend It is categorized as a trend because the stock prices experienced upward and downward movements that occurred recurrently.
During the first half of 2020, the prices This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
showed a declining trend, whereas from 2021 to 2023, they demonstrated an upward trend.
Therefore, the use of Support Vector Regression (SVR) and Double Exponential Smoothing (DES) methods is considered appropriate for forecasting BRIAos daily closing stock prices.
Analysis of the SVR Method Selection of the Best Model Using Grid Search Optimization Grid Search is employed to identify the optimal parameters for a model so that the selected model can accurately predict the data.
The optimization of the SVR model using Grid Search requires parameters that are adjusted to the type of kernel applied.
Grid Search Optimization is performed using the k-fold cross-validation technique.
The Grid Search process is adjusted according to the kernel used in the modeling.
For the linear kernel.
Grid Search is used to determine the most optimal values of C and A.
A very large C value neglects the maximum margin variations, leading to constant errors.
Conversely, a very small C value places too much emphasis on penalties in SVR.
Meanwhile, a smaller A restricts the tolerance for errors, while a larger A increases the allowable error tolerance.
For polynomial, sigmoid, and radial kernels.
Grid Search is used to determine the optimal values of C.
A, and .
The parameter specifies the influence of each data point when mapping the input space to higher dimensions.
Table 2: Results of Grid Search Parameters Kernel Linear Polynomial Radial Sigmoid Best yu Best C Best yu Smallest Error From Table 2, it can be observed that for the linear kernel, the smallest error .
was obtained when k = 2 with parameters A = 0.
1 and C = 0.
For the polynomial kernel, the best parameters were A = 0.
C = 100, and = 3, producing an error of 0.
02057196 at k = 8.
Meanwhile, the radial kernel yielded the smallest error of 0.
00096087 with parameters A = 0.
C = 100, and = 10 at k = 3.
Finally, the sigmoid kernel resulted in an error of 06809274 at k = 2 with parameters A = 0.
C = 0.
05, and = 1.
Based on these results, the radial kernel was selected as the most suitable kernel, with parameters A = 0.
C = 100, and = 10 at k = 3, as it provided the lowest error compared to other kernels.
2 Stock Price Forecasting The optimal parameters obtained in the previous step were used to conduct stock price The forecasting results are presented in Figure 2.
This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
Figure 2: Plot of Predicted Values Against Actual Data As shown in Figure 2, the red points represent the predicted values, while the black points represent the actual data.
The figure indicates that the forecasting results closely follow the actual data.
A comparison between the predicted and actual values of the stock closing price is presented in Table 3.
Table 3: Forecasting Results of BRI Stock Closing Prices Using SVR Date 1 Dec 2023 4 Dec 2023 5 Dec 2023 6 Dec 2023 7 Dec 2023 8 Dec 2023 11 Dec 2023 12 Dec 2023 13 Dec 2023 14 Dec 2023 15 Dec 2023 18 Dec 2023 19 Dec 2023 20 Dec 2023 21 Dec 2023 22 Dec 2023 27 Dec 2023 28 Dec 2023 29 Dec 2023 Predicted Value 5068,983 5185,228 5163,271 5139,612 5161,662 5067,308 5021,792 5232,328 5257,600 5185,181 5253,418 5232,331 5281,175 5350,242 5328,305 5350,242 5328,305 5397,346 5422,518 Actual Value 5077,939 5220,311 5172,854 5149,125 5196,583 5101,668 5030,482 5054,210 5030,482 5267,769 5267,769 5220,311 5267,769 5267,769 5291,497 5386,412 5338,955 5433,869 5433,869 From Table 6, it can be observed that the predicted values are very close to the actual values, indicating that the selected parameters are well-suited for the dataset.
To further assess forecasting accuracy, the Mean Absolute Percentage Error (MAPE) was calculated using RStudio software.
The resulting MAPE value was 0.
3561446% OO 0.
35%, which falls well below 10%, thereby confirming that the forecasting accuracy is excellent.
Analysis of the DES Method Parameters of the DES Method In the Double Exponential Smoothing (DES) method, past data are weighted exponentially using two smoothing parameters, namely and .
A trial-and-error process was conducted by combining different values of and to obtain the most optimal parameter combination, with the computation performed using RStudio software.
After testing various parameter combinations, the next step was to select the best forecasting model based on the smallest Mean Absolute Percentage Error (MAPE).
The results of the parameter testing are presented in Table 4.
Table 3: Forecasting Results of BRI Stock Closing Prices Using DES This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
Alpha
Beta
MAPE (%)
As shown in Table 3, the smallest MAPE value was obtained at = 0.
99 and = 0.
05, yielding a MAPE of 4.
Therefore, the best forecasting model was achieved with parameters = 0.
99 and = 0.
Parameters of the DES Method Subsequently, the smoothing values for level and trend were calculated using the optimal parameters obtained previously, namely = 0.
99 and = 0.
The results of the level smoothing, trend smoothing, and forecasts are presented in Table 4 Table 4: Smoothing Values for Level.
Trend, and Forecasts Period Level Smoothing .
A Trend Smoothing .
cyei ) A Forecast As illustrated in Table 4, the smoothing process captures both the level and trend components of the BRI stock closing price series.
These values provide the foundation for generating accurate forecasts in subsequent periods.
Parameters of the DES Method After the data smoothing process, the next step is to perform forecasting for the upcoming period using the parameters =0.
89 and =0.
The forecasting results are presented in Figure 3.
This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
Figure 3: Forecasting Result of BRI Closing Stock Prices Based on Figure 3, the blue line represents the actual data or the closing stock price data from January 2020 to November 2023.
The red line indicates the fitted values, which follow the trend of the actual data quite well, while the green line represents the forecasted data for the upcoming month.
From the forecast plot, it can be observed that within the next month, the plot exhibits a relatively stable upward movement, indicating that BRIAos stock price is expected to gradually increase.
The detailed forecasting results are shown in Table 5 Table 5: Forecasting Results Using the DES Method Date 1 Dec 2023 4 Dec 2023 5 Dec 2023 6 Dec 2023 7 Dec 2023 8 Dec 2023 11 Dec 2023 12 Dec 2023 13 Dec 2023 14 Dec 2023 15 Dec 2023 18 Dec 2023 19 Dec 2023 20 Dec 2023 21 Dec 2023 22 Dec 2023 27 Dec 2023 28 Dec 2023 29 Dec 2023 Forecast From Table 5, it can be seen that the forecasted closing stock prices of BRI demonstrate a consistent upward trend throughout December 2023.
Starting from IDR 4,988.
28 on December 1, 2023, the price is projected to gradually increase and reach IDR 5,031.
42 by December 29, 2023.
This steady upward trajectory suggests that the DES method successfully captures the positive momentum in the stockAos movement.
The relatively small incremental increases also imply stability, indicating that BRIAos stock price is unlikely to experience abrupt fluctuations in the short term.
Such information may provide useful insights for investors and policymakers in anticipating short-term market dynamics.
This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
Selection of The Best Method The selection of the best method between SVR and DES is carried out by comparing the MAPE values.
Based on both methods, the best model is determined by the smallest MAPE value from each model.
The comparison results of the MAPE values from the two methods are presented in Table 6 Table 6: Comparison of MAPE Values Method Support Vector Regression Double Exponential Smoothing MAPE Value (%) Based on Table 10, it is shown that the Support Vector Regression method produces a MAPE value of 0.
3561%, while the Double Exponential Smoothing method produces a MAPE value Thus, it can be concluded that Support Vector Regression has the smallest MAPE value, which means that this method is the best in forecasting BRIAos closing stock Discussion Based on BRIAos daily closing stock price data from January 2020 to November 2023 obtained from the Yahoo Finance website, both the Support Vector Regression (SVR) and Double Exponential Smoothing (DES) methods were applied.
The descriptive analysis results show that the average daily closing stock price during the period was IDR 3,683 per share, with the lowest closing price of IDR 1,655 per share on May 18, 2020, and the highest closing price of IDR 5,410 per share in August 2023.
According to Figure 4.
1, which displays the plot of BRIAos closing stock prices, at the beginning of 2020 the stock price experienced a significant decline, largely due to the impact of the COVID-19 pandemic (Febrianty Lautania et al.
However, after reaching its lowest point, the stock price gradually recovered and continued to rise until the end of 2020.
In 2021 and 2022, the upward trend persisted despite some fluctuations.
Furthermore, in 2023.
BRIAos stock price showed a consistent increase throughout the period.
In the Support Vector Regression method, the best model for each kernel was obtained as follows: for the linear kernel.
A=0.
1 and C=0.
05 with an error of 0.
for the polynomial kernel.
A=0.
C=100, and =3 with an error of 0.
for the radial kernel.
A=0.
C=100, and =10 with an error of 0.
and for the sigmoid kernel.
A=0.
C=0.
05, and =1 with an error of 0.
Based on these results, it can be concluded that the most appropriate kernel for forecasting is the radial kernel.
This conclusion is consistent with studies conducted by Hermawan et al.
and Purnama & Hendarsin .
, which also found that the RBF kernel provides the best accuracy compared to linear or polynomial kernels.
The testing results of the best model applied to the actual data yielded an accuracy level of 3561446, which effectively followed the actual data patterns, as also illustrated in Figure 4.
where the forecast values closely approximated the actual data.
Thus, the forecasting results of BRIAos daily closing stock prices for December 2023 indicated unstable changes over the upcoming month.
Meanwhile, the Double Exponential Smoothing method applied the best parameter combination obtained through trial and error across all and values, with the optimal combination being =0.
99 and =0.
The forecasting results indicate that during December 2023, the stock prices are expected to increase gradually, reflecting a slow upward trend in BRIAos closing stock prices.
By comparing the forecasting accuracy based on the MAPE values of both methods, it was found that the Support Vector Regression method achieved a MAPE of 0.
3561%, while the Double Exponential Smoothing method achieved a MAPE of 4.
Therefore, it can be This open access article is distributed under a Creative Commons Attribution (CC-BY-NC) 4.
Meliyana, et.
ARRUS Journal of Mathematics and Applied Science.
Vol.
No.
https://doi.
org/10.
35877/mathscience4282 ISSN : 2776-7922 (Prin.
/ 2807-3037 (Onlin.
concluded that the Support Vector Regression method outperforms the Double Exponential Smoothing method in forecasting BRIAos daily closing stock prices.
Conclusion Based on the results and discussion of forecasting BRIAos daily closing stock prices, the following conclusions can be drawn:
Forecasting using the Support Vector Regression (SVR) method produced the best model with the radial kernel, using the parameters A=0.
C=100, and =10.
Based on the forecasting results with the best model, it was found that the forecasted BRI closing stock prices for December 2023 indicated unstable changes.
Forecasting using the Double Exponential Smoothing (DES) method produced the best parameter combination of =0.
99 and =0.
Based on the forecasting results, it was found that BRIAos daily closing stock prices in December 2023 are expected to gradually .
Forecasting with the Support Vector Regression method resulted in an accuracy level with a MAPE of 0.
3561%, whereas the Double Exponential Smoothing method produced an accuracy level with a MAPE of 4.
This means that the best method for forecasting BRIAos daily closing stock prices is the Support Vector Regression method.
References