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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Parameter: Jurnal Matematika, Statistika dan Terapannya
Wisnowan Hendy Saputra
Computer Science Department, School of Computer Science, Bina Nusantara University, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Cluster Analysis on Time Series Data for Indonesian Stock Prices Using Dynamic Time Warping Wisnowan Hendy Saputra; Nuruddeen Shehu
Parameter: Jurnal Matematika, Statistika dan Terapannya Vol 5 No 1 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/parameterv5i1pp01-16

Abstract

This study investigates the application of the Dynamic Time Warping (DTW) algorithm to cluster the ten stocks with the largest market capitalization on the Indonesia Stock Exchange as of February 2026. Unlike conventional distance metrics, DTW handles time lag nonlinearly to identify hidden temporal pattern similarities. Adjusted closing price data was obtained through web scraping from Yahoo Finance using the R programming language. The clustering procedure was performed using Ward's Hierarchical Agglomerative Clustering method, where the number of clusters was evaluated through Silhouette coefficient analysis and qualitative economic interpretability. While the highest Silhouette score suggested two clusters, a three-cluster solution was selected as the most representative structure to better capture the granular dynamics of different market sectors. The first cluster is dominated by the banking and energy sectors with stable growth trends. The second cluster includes cyclical industrial and infrastructure stocks with high volatility. The third cluster uniquely unites GOTO and UNVR stocks in a long-term bearish downward pattern, despite their origins in different sectors. These findings demonstrate that DTW is highly effective in uncovering cross-sector market dynamics, providing a more accurate basis for portfolio diversification strategies than traditional business sector classifications.
MODIFIED STATISTICAL-BASED VALUE AT RISK FOR MULTI-OBJECTIVE OPTIMAL-BASED PORTFOLIO ANALYSIS OF INDONESIAN STOCK RETURN DISTRIBUTION Wisnowan Hendy Saputra; Hasri Wiji Aqsari
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0287-0298

Abstract

Basically, all stock investments aim to obtain maximum profit with low risk. The formation of a stock investment portfolio is always accompanied by measuring returns and risks that show its performance. Portfolio risk measurement is often faced with the challenge that returns are not normally distributed, so that measurements using the normality assumption cannot be applied. This study proposes the development of a modification of stock portfolio risk measurement so that it is not limited to the normality assumption. The development is carried out by modifying the calculation of Value at Risk (VaR) to consider the skewness and kurtosis values ​​(hereinafter referred to as modified VaR), so that the normal distribution assumption can be eliminated. As a method for compiling a stock portfolio, the Multi-Objective Optimization technique was chosen because it can modify risk averse so that the risk can be adjusted to the risk profile of each investor and is able to stabilize the mean return value. For its implementation, this paper uses real stock data which of course has returns that are not normally distributed, namely the four Indonesian stocks based on the largest capitalization recorded in January 2025 (blue chip), namely BREN, BBCA, BYAN, and BBRI obtained through finance.yahoo.com. The analysis method is divided into three steps, including multi-objective optimization completion, portfolio return calculation, and finally modified VaR estimation. The results of the study show that BBCA has the largest weight with a portion of more than 40% of the four stocks, so BBCA will be the priority stock for this portfolio. The portfolio formed using multi-objective optimization is proven to have a stable mean return because the portfolio mean return is between several of its constituent stocks (vice versa) which is around 0.01%, and the smallest estimated value of the portfolio modified VaR is 1.67%. Thus, a portfolio based on multi-objective optimization is not only able to create a portfolio that provides a small risk in risk measurement without assuming a normal distribution, but at the same time multi-objective optimization is also able to provide competitive returns with its constituent stocks.
Co-Authors Hasri Wiji Aqsari Nuruddeen Shehu