BIST30'da Portföy Çeşitlendirmesi için Dinamik Zaman Bükme Algoritması: Metodolojik Bir Yaklaşım
Yıl 2025,
Cilt: 25 Sayı: 1, 97 - 110, 25.03.2025
İsmail Çelik
,
Arife Özdemir Höl
,
Semra Demir
Öz
Bu çalışma, finansal varlıkların doğrusal olmayan yapılarını dikkate alarak çeşitlendirme stratejisi sunan Dinamik Zaman Bükme (DTW) algoritmasının, geleneksel Markowitz portföy çeşitlendirme stratejisine üstünlük sağlayıp sağlamadığını araştırmaktadır. Bu doğrultuda, Borsa İstanbul'da işlem gören BIST30 endeksi kapsamındaki 20 şirketin 01.01.2018-01.01.2024 dönemine ait günlük hisse senedi fiyat verileri kullanılarak portföyler oluşturulmuş ve performansları karşılaştırılmıştır.
Elde edilen bulgular, DTW algoritmasının özellikle boğa piyasalarında daha yüksek kümülatif getiriler sağladığını, ancak bu getirilerin daha yüksek volatilite ve risk ile birlikte geldiğini göstermektedir. Diğer taraftan, Markowitz yöntemi, daha düşük volatilite ve daha dengeli getiriler sunarak ayı piyasalarında daha istikrarlı bir performans sergilemektedir.
Çalışmanın sonuçları, yatırımcıların farklı piyasa koşullarına etkili bir şekilde uyum sağlayarak portföy performanslarını artırmalarına yardımcı olacak alternatif portföy optimizasyon stratejileri sunmaktadır.
Etik Beyan
Bu çalışmanın bilimsel etik kurallara ve bilimsel yönteme uyularak hazırlanan özgün nitelikte bir araştırma makalesi olduğunu, başka hiçbir dergide yayınlanmadığını veya sunulmadığını, etik ve bilimsel açıdan sorumluluğun makalenin tüm yazarlarına ait olduğunu kabul ederiz.
Destekleyen Kurum
Yazarlar, bu araştırmayı desteklemek için herhangi bir dış fon almadıklarını kabul ederler
Kaynakça
- Aghabozorgi, S., Shirkhorshidi, A. S., ve Wah, T. Y. (2015), Time-Series Clustering–A Decade Review, Information systems, 53, s.16-38.
- Babiš, A., ve Stehlíková, B. (2021), Time Series Clustering Based on Time-Varying Hurst Exponent, Advances in Methodology & Statistics/Metodološki Zvezki, 18(2), s.73-88. https://doi.org/10.51936/gktc3784.
- Bai, L., Cui, L., Zhang, Z., Xu, L., Wang, Y., ve Hancock, E. R. (2020), Entropic Dynamic Time Warping Kernels for Co-Evolving Financial Time Series Analysis, IEEE Transactions on Neural Networks and Learning Systems,
34(4), s.1808-1822.
- Berndt, D. J., ve Clifford, J. (1994), Using Dynamic Time Warping to Find Patterns in Time Series, In Proceedings
of the 3rd international conference on knowledge discovery and data mining, s.359-370.
- Brodie, J., Daubechies, I., Mol, C. D., Giannone, D., ve Loris, I, (2009), Sparse and Stable Markowitz Portfolios,
Proceedings of the National Academy of Sciences, 106(30), s.12267-12272.
https://doi.org/10.1073/pnas.0904287106
- Caferra, R., Tedeschi, G., ve Morone, A. (2021), Bitcoin: Bubble that Bursts or Gold that Glitters?, Economics
Letters, 205, 109942, s.1-4. https://doi.org/10.1016/j.econlet.2021.109942
- Demirtaş, Ö., ve Güngör, Z. (2004), Portföy Yönetimi ve Portföy Seçimine Yönelik Uygulama, Journal of
Aeronautics and Space Technologies, 1(4), s.103-109.
- Engle, R., ve Russell, J. (1998), Autoregressive Conditional Duration: A New Model for Irregularly Spaced
Transaction Data, Econometrica, 66(5), 1127, s.1127-1162. https://doi.org/10.2307/2999632
- Eom, C., Park, J. W., Kim, Y. H., ve Kaizoji, T. (2015), Effects of the Market Factor on Portfolio Diversification: The
Case of Market Crashes, Investment Analysts Journal, 44(1), s.71-83.
https://doi.org/10.1080/10293523.2015.994448
- Fedorovich, O., Uruskiy, O., Pronchakov, Y., ve Lukhanin, M. I. (2021), Method and Information Technology to
Research the Component Architecture of Products to Justify İnvestments of High-Tech Enterprise,
Radioelectronic and Computer Systems, (1), s.150-157. https://doi.org/10.32620/reks.2021.1.13.
- Feng, L., Zhao, X., Liu, Y., Yao, Y., ve Jin, B. (2010), A Similarity Measure of Jumping Dynamic Time Warping, 2010
Seventh International Conference on Fuzzy Systems and Knowledge Discovery.
https://doi.org/10.1109/fskd.2010.5569383.
- Feng, Q. (2022), Optimal Portfolio Construction Based on Markowitz Model, BCP Business &Amp; Management,
35, s.273-280. https://doi.org/10.54691/bcpbm.v35i.3303.
- Franses, P., ve McAleer, M. (2002), Financial Volatility: An Introduction, Journal of Applied Econometrics, 17(5),
s.419-424. https://doi.org/10.1002/jae.693.
- Grzejszczak, T., Probierz, E., Gałuszka, A., Simek, K., Jędrasiak, K., ve Wiśniewski, T. (2022), Dynamic Time Warping
in Financial Data: Modification of Algorithm in Context of Stock Market Similarity Analysis, European Research
Studies Journal, XXV (1), s.967-979.
- Guan, H. ve Jiang, Q. (2007), Cluster Financial Time Series for Portfolio, 2007 International Conference on
Wavelet Analysis and Pattern Recognition. https://doi.org/10.1109/icwapr.2007.4420788.
- Guan, J., He, J., Peng, S., ve Xue, T. (2022), Comparisons to Investment Portfolios under Markowitz Model and
Index Model Based on US’s Stock Market, BCP Business &Amp; Management, 26, s.905-915.
https://doi.org/10.54691/bcpbm.v26i.2053.
- Gubu, L., Rosadi, D., ve Abdurakhman, A. (2021a), Robust Portfolio Selection with Clustering Based on Business Sector of Stocks, Media Statistika, 14(1), s.33-43.
- Gubu, L., Rosadi, D., ve Abdurakhman, A. (2021b), Pembentukan Portofolio Saham Menggunakan Klastering Time Series K-Medoid Dengan Ukuran Jarak Dynamic Time Warping, Jurnal Aplikasi Statistika & Komputasi
Statistik, 13(2), s.35-46. https://doi.org/10.34123/jurnalasks.v13i2.295
- He, H., ve Li, H. (2023), A New Boosting Algorithm for Online Portfolio Selection Based on Dynamic Time Warping and Anti-Correlation, Computational Economics, 63, s.1777-1803. https://doi.org/10.1007/s10614-023-10383-6.
- Henkin, R., ve Barnes, M. (2022), Visxhclust: An R Shiny Package for Visual Exploration of Hierarchical Clustering, The Journal of Open Source Software, 7(70), 4074, s.1-4. https://doi.org/10.21105/joss.04074.
- Hsu, C., Huang, K., Yang, C., ve Guo, Y. (2015), Flexible Dynamic Time Warping for Time Series Classification,
Procedia Computer Science, 51, s.2838-2842. https://doi.org/10.1016/j.procs.2015.05.444.
- Jeong, Y. S., Jeong, M. K., ve Omitaomu, O. A. (2011), Weighted Dynamic Time Warping for Time Series
Classification, Pattern recognition, 44(9), s.2231-2240.
- Kallio, M. ve Hardoroudi, N. D. (2019), Advancements in Stochastic Dominance Efficiency Tests, European
Journal of Operational Research, 276(2), s.790-794. https://doi.org/10.1016/j.ejor.2018.12.014.
- Kate, R. J. (2016), Using Dynamic Time Warping Distances As Features for Improved Time Series Classification,
Data mining and knowledge discovery, 30, s.283-312.
- Keogh, E. ve M. Pazzani. (2001), Derivative Dynamic Time Warping, In Proc. of the First Intl. SIAM Intl. Conf. on
Data Mining, Chicago, Illinois.
- Keogh, E. J., ve Pazzani, M. J. (1999), Scaling up Dynamic Time Warping to Massive Datasets, In Principles of
Data Mining and Knowledge Discovery: Third European Conference, PKDD’99, Prague, Czech Republic,
September 15-18. Proceedings 3, s.1-11. Springer Berlin Heidelberg.
- Keogh, E., ve Ratanamahatana, C. A. (2005), Exact Indexing of Dynamic Time Warping, Knowledge and information systems, 7, s.358-386. doi: 10.1007/s10115-004-0154-9.
- Keykhaei, R. (2016), Mean-variance Portfolio Optimization When Each Asset Has Individual Uncertain Exit-
Time, Pakistan Journal of Statistics and Operation Research, 12(4), s.765-773.
https://doi.org/10.18187/pjsor.v12i4.1251.
- Kim, S. H., Lee, H. S., Ko, H. J., Jeong, S., Byun, H. W., ve Oh, K. J. (2018), Pattern Matching Trading System Based
on the Dynamic Time Warping Algorithm, Sustainability, 10(12), 4641, s.1-18. https://doi.org/10.3390/su10124641.
- Kulkarni, N. (2017), Effect of Dynamic Time Warping Using Different Distance Measures on Time Series
Classification, International Journal of Computer Applications, 179(6), s.34-39.
https://doi.org/10.5120/ijca2017915974.
- Kuo, C., ve Davidson, I. (2018), On the Equivalence of Tries and Dendrograms- Efficient Hierarchical Clustering
of Traffic Data, s.1-9. https://doi.org/10.48550/arxiv.1810.05357.
- Lampert, T., Lafabregue, B., ve Gançarski, P. (2019), Constrained Distance Based K-Means Clustering for
Satellite Image Time-Series, In IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing
Symposium (pp. 2419-2422). IEEE.
- Li, H. (2021), Time Works Well: Dynamic Time Warping Based on Time Weighting for Time Series Data Mining,
Information Sciences, 547, s.592-608.
- Liao, T. W. (2005), Clustering of Time Series Data—A Survey, Pattern recognition, 38(11), s.1857-1874.
doi:10.1016/j.patcog.2005.01.025
- Ling, S., McAleer, M., ve Tong, H. (2015), Frontiers in Time Series and Financial Econometrics: An Overview,
Journal of Econometrics, 189(2), s.245-250. https://doi.org/10.1016/j.jeconom.2015.03.019.
- Liu, L., Li, W., ve Jia, H. (2018), Method of Time Series Similarity Measurement Based on Dynamic Time Warping,
Computers, Materials & Continua, 57(1), s.97-106. doi:10.32604/cmc.2018.03511.
- Lucarelli, G., ve Borrotti, M. (2020), A Deep Q-Learning Portfolio Management Framework for the
Cryptocurrency Market, Neural Computing and Applications, 32(23), s.17229-17244.
https://doi.org/10.1007/s00521-020-05359-8.
- Luo, J. (2021), A Study on Stock Graph Recognition Based on Wavelet Denoising and DTW Algorithm,
Mathematical Problems in Engineering, 2021, s.1-15. https://doi.org/10.1155/2021/6641749.
- Markowitz, H. (1952), Portfolio Selection, The Journal of Finance, 7(1), s.77–91. https://doi.org/10.2307/2975974
- Massahi, M., Mahootchi, M., ve Arshadi Khamseh, A. (2020), Development of an Efficient Cluster-Based
Portfolio Optimization Model Under Realistic Market Conditions, Empirical Economics, 59(5), s.2423-2442.
https://doi.org/10.1007/s00181-019-01802-5
- Montenegro, M., ve Albuquerque, P. (2017), Wealth Management: Modeling the Nonlinear Dependence,
Algorithmic Finance, 6(1-2), s.51-65. https://doi.org/10.3233/af-170203
- Nanda, S. R., Mahanty, B., ve Tiwari, M. K. (2010), Clustering Indian Stock Market Data for Portfolio Management,
Expert Systems with Applications, 37(12), s.8793-8798. https://doi.org/10.1016/j.eswa.2010.06.026.
- Nugraha, E. (2024), Portfolio Optimization Analysis Using Markowitz Model on IDX30 Stock Index in 2022 and
2023, Firm Journal of Management Studies, 9(1), 97. https://doi.org/10.33021/firm.v9i1.4990.
- Platanakis, E., ve Urquhart, A. (2020), Should Investors Include Bitcoin in Their Portfolios? a Portfolio Theory
Approach, The British Accounting Review, 52(4), 100837, s.1-19. https://doi.org/10.1016/j.bar.2019.100837.
- Ratanamahatana, C. A. ve Keogh, E. (2004), Making Time-Series Classification More Accurate Using Learned
Constraints, Proceedings of the 2004 SIAM International Conference on Data Mining.
https://doi.org/10.1137/1.9781611972740.2.
- Sakoe, H., ve Chiba, S. (1978), Dynamic Programming Algorithm Optimization for Spoken Word Recognition,
IEEE transactions on acoustics, speech, and signal processing, 26(1), s.43-49.
- Salvador, S., ve Chan, P. (2007), Toward Accurate Dynamic Time Warping in Linear Time and Space, Intelligent
Data Analysis, 11(5), s.561-580. DOI: 10.3233/IDA-2007-11508.
- Shirota, Y., ve Murakami, A. (2021), Long-term Time Series Data Clustering of Stock Prices for Portfolio
Selection, In 2021 IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI) 1-
6.
- Širůček, M., ve Křen, L. (2017), Application of Markowitz Portfolio Theory by Building Optimal Portfolio on the US
Stock Market, J. Stanković, P. Delias, S. Marinković, S. Rochhia (Eds.), In Tools and Techniques for Economic
Decision Analysis (pp. 24-42). IGI Global.
- Tatsat, H., Puri, S., ve Lookabaugh, B. (2020), Machine Learning and Data Science Blueprints for Finance,
O'Reilly media.
- Tayalı, S. T. (2020), A Novel Backtesting Methodology for Clustering in Mean–Variance Portfolio Optimization, Knowledge-Based Systems, 209, s.1-12. https://doi.org/10.1016/j.knosys.2020.106454
- Torre-Torres, O. V. D. l., Figueroa, E. G., ve Montoya, D. A. (2015), An Actual Position Benchmark for Mexican Pension Funds Performance, Economía Teoría Y Práctica, (43). https://doi.org/10.24275/etypuam/ne/432015/delatorre.
- Vaclavik, M., ve Jablonsky, J. (2012) Revisions of Modern Portfolio Theory Optimization Model, Central European
journal of operations research, 20, s.473-483. DOI 10.1007/s10100-011-0227-2.
- Vahidipour, S., Mirzaei, A., ve Rahmati, M. (2014), Comparing Weighted Combination of Hierarchical Clustering
Based on Cophenetic Measure, Intelligent Data Analysis, 18(4), s.547-559. https://doi.org/10.3233/ida-1406,57.
- Wang, Y. (2023), Select the Optimal Portfolio by Analyzing and Comparing the Better Performance of
Markowitz Model and Index Model Under 5 Different Constraints, Advances in Economics, Management and
Political Sciences, 13(1), s.364-376. https://doi.org/10.54254/2754-1169/13/20230753.
- Xu, Y., Zhao, X., Chen, Y., ve Yang, Z. (2019), Research on A Mixed Gas Classification Algorithm Based on
Extreme Random Tree, Applied Sciences, 9(9), 1728, s.1-17. https://doi.org/10.3390/app9091728.
Dynamic Time Warping Algorithm for Portfolio Diversification in BIST30: A Methodological Approach
Yıl 2025,
Cilt: 25 Sayı: 1, 97 - 110, 25.03.2025
İsmail Çelik
,
Arife Özdemir Höl
,
Semra Demir
Öz
This paper investigates whether the Dynamic Time Warping (DTW) algorithm, which provides a diversification strategy by taking into account the nonlinear structure of financial assets, is superior to the traditional Markowitz portfolio diversification strategy. In this regard, portfolios were constructed and their performances were evaluated through a comparison of the daily stock price data of 20 companies within the scope of the BIST30 index traded in Borsa Istanbul over the period from 01/01/2018 to 01/01/2024.
The findings show that the DTW algorithm provides higher cumulative returns, especially in bull markets, but these returns come with higher volatility and risk. On the other hand, the Markowitz method is more consistent in bear markets, offering lower volatility and more stable returns.
The results of the study provide alternative portfolio optimization strategies to help investors improve their portfolio performance by effectively adapting to different market conditions.
Kaynakça
- Aghabozorgi, S., Shirkhorshidi, A. S., ve Wah, T. Y. (2015), Time-Series Clustering–A Decade Review, Information systems, 53, s.16-38.
- Babiš, A., ve Stehlíková, B. (2021), Time Series Clustering Based on Time-Varying Hurst Exponent, Advances in Methodology & Statistics/Metodološki Zvezki, 18(2), s.73-88. https://doi.org/10.51936/gktc3784.
- Bai, L., Cui, L., Zhang, Z., Xu, L., Wang, Y., ve Hancock, E. R. (2020), Entropic Dynamic Time Warping Kernels for Co-Evolving Financial Time Series Analysis, IEEE Transactions on Neural Networks and Learning Systems,
34(4), s.1808-1822.
- Berndt, D. J., ve Clifford, J. (1994), Using Dynamic Time Warping to Find Patterns in Time Series, In Proceedings
of the 3rd international conference on knowledge discovery and data mining, s.359-370.
- Brodie, J., Daubechies, I., Mol, C. D., Giannone, D., ve Loris, I, (2009), Sparse and Stable Markowitz Portfolios,
Proceedings of the National Academy of Sciences, 106(30), s.12267-12272.
https://doi.org/10.1073/pnas.0904287106
- Caferra, R., Tedeschi, G., ve Morone, A. (2021), Bitcoin: Bubble that Bursts or Gold that Glitters?, Economics
Letters, 205, 109942, s.1-4. https://doi.org/10.1016/j.econlet.2021.109942
- Demirtaş, Ö., ve Güngör, Z. (2004), Portföy Yönetimi ve Portföy Seçimine Yönelik Uygulama, Journal of
Aeronautics and Space Technologies, 1(4), s.103-109.
- Engle, R., ve Russell, J. (1998), Autoregressive Conditional Duration: A New Model for Irregularly Spaced
Transaction Data, Econometrica, 66(5), 1127, s.1127-1162. https://doi.org/10.2307/2999632
- Eom, C., Park, J. W., Kim, Y. H., ve Kaizoji, T. (2015), Effects of the Market Factor on Portfolio Diversification: The
Case of Market Crashes, Investment Analysts Journal, 44(1), s.71-83.
https://doi.org/10.1080/10293523.2015.994448
- Fedorovich, O., Uruskiy, O., Pronchakov, Y., ve Lukhanin, M. I. (2021), Method and Information Technology to
Research the Component Architecture of Products to Justify İnvestments of High-Tech Enterprise,
Radioelectronic and Computer Systems, (1), s.150-157. https://doi.org/10.32620/reks.2021.1.13.
- Feng, L., Zhao, X., Liu, Y., Yao, Y., ve Jin, B. (2010), A Similarity Measure of Jumping Dynamic Time Warping, 2010
Seventh International Conference on Fuzzy Systems and Knowledge Discovery.
https://doi.org/10.1109/fskd.2010.5569383.
- Feng, Q. (2022), Optimal Portfolio Construction Based on Markowitz Model, BCP Business &Amp; Management,
35, s.273-280. https://doi.org/10.54691/bcpbm.v35i.3303.
- Franses, P., ve McAleer, M. (2002), Financial Volatility: An Introduction, Journal of Applied Econometrics, 17(5),
s.419-424. https://doi.org/10.1002/jae.693.
- Grzejszczak, T., Probierz, E., Gałuszka, A., Simek, K., Jędrasiak, K., ve Wiśniewski, T. (2022), Dynamic Time Warping
in Financial Data: Modification of Algorithm in Context of Stock Market Similarity Analysis, European Research
Studies Journal, XXV (1), s.967-979.
- Guan, H. ve Jiang, Q. (2007), Cluster Financial Time Series for Portfolio, 2007 International Conference on
Wavelet Analysis and Pattern Recognition. https://doi.org/10.1109/icwapr.2007.4420788.
- Guan, J., He, J., Peng, S., ve Xue, T. (2022), Comparisons to Investment Portfolios under Markowitz Model and
Index Model Based on US’s Stock Market, BCP Business &Amp; Management, 26, s.905-915.
https://doi.org/10.54691/bcpbm.v26i.2053.
- Gubu, L., Rosadi, D., ve Abdurakhman, A. (2021a), Robust Portfolio Selection with Clustering Based on Business Sector of Stocks, Media Statistika, 14(1), s.33-43.
- Gubu, L., Rosadi, D., ve Abdurakhman, A. (2021b), Pembentukan Portofolio Saham Menggunakan Klastering Time Series K-Medoid Dengan Ukuran Jarak Dynamic Time Warping, Jurnal Aplikasi Statistika & Komputasi
Statistik, 13(2), s.35-46. https://doi.org/10.34123/jurnalasks.v13i2.295
- He, H., ve Li, H. (2023), A New Boosting Algorithm for Online Portfolio Selection Based on Dynamic Time Warping and Anti-Correlation, Computational Economics, 63, s.1777-1803. https://doi.org/10.1007/s10614-023-10383-6.
- Henkin, R., ve Barnes, M. (2022), Visxhclust: An R Shiny Package for Visual Exploration of Hierarchical Clustering, The Journal of Open Source Software, 7(70), 4074, s.1-4. https://doi.org/10.21105/joss.04074.
- Hsu, C., Huang, K., Yang, C., ve Guo, Y. (2015), Flexible Dynamic Time Warping for Time Series Classification,
Procedia Computer Science, 51, s.2838-2842. https://doi.org/10.1016/j.procs.2015.05.444.
- Jeong, Y. S., Jeong, M. K., ve Omitaomu, O. A. (2011), Weighted Dynamic Time Warping for Time Series
Classification, Pattern recognition, 44(9), s.2231-2240.
- Kallio, M. ve Hardoroudi, N. D. (2019), Advancements in Stochastic Dominance Efficiency Tests, European
Journal of Operational Research, 276(2), s.790-794. https://doi.org/10.1016/j.ejor.2018.12.014.
- Kate, R. J. (2016), Using Dynamic Time Warping Distances As Features for Improved Time Series Classification,
Data mining and knowledge discovery, 30, s.283-312.
- Keogh, E. ve M. Pazzani. (2001), Derivative Dynamic Time Warping, In Proc. of the First Intl. SIAM Intl. Conf. on
Data Mining, Chicago, Illinois.
- Keogh, E. J., ve Pazzani, M. J. (1999), Scaling up Dynamic Time Warping to Massive Datasets, In Principles of
Data Mining and Knowledge Discovery: Third European Conference, PKDD’99, Prague, Czech Republic,
September 15-18. Proceedings 3, s.1-11. Springer Berlin Heidelberg.
- Keogh, E., ve Ratanamahatana, C. A. (2005), Exact Indexing of Dynamic Time Warping, Knowledge and information systems, 7, s.358-386. doi: 10.1007/s10115-004-0154-9.
- Keykhaei, R. (2016), Mean-variance Portfolio Optimization When Each Asset Has Individual Uncertain Exit-
Time, Pakistan Journal of Statistics and Operation Research, 12(4), s.765-773.
https://doi.org/10.18187/pjsor.v12i4.1251.
- Kim, S. H., Lee, H. S., Ko, H. J., Jeong, S., Byun, H. W., ve Oh, K. J. (2018), Pattern Matching Trading System Based
on the Dynamic Time Warping Algorithm, Sustainability, 10(12), 4641, s.1-18. https://doi.org/10.3390/su10124641.
- Kulkarni, N. (2017), Effect of Dynamic Time Warping Using Different Distance Measures on Time Series
Classification, International Journal of Computer Applications, 179(6), s.34-39.
https://doi.org/10.5120/ijca2017915974.
- Kuo, C., ve Davidson, I. (2018), On the Equivalence of Tries and Dendrograms- Efficient Hierarchical Clustering
of Traffic Data, s.1-9. https://doi.org/10.48550/arxiv.1810.05357.
- Lampert, T., Lafabregue, B., ve Gançarski, P. (2019), Constrained Distance Based K-Means Clustering for
Satellite Image Time-Series, In IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing
Symposium (pp. 2419-2422). IEEE.
- Li, H. (2021), Time Works Well: Dynamic Time Warping Based on Time Weighting for Time Series Data Mining,
Information Sciences, 547, s.592-608.
- Liao, T. W. (2005), Clustering of Time Series Data—A Survey, Pattern recognition, 38(11), s.1857-1874.
doi:10.1016/j.patcog.2005.01.025
- Ling, S., McAleer, M., ve Tong, H. (2015), Frontiers in Time Series and Financial Econometrics: An Overview,
Journal of Econometrics, 189(2), s.245-250. https://doi.org/10.1016/j.jeconom.2015.03.019.
- Liu, L., Li, W., ve Jia, H. (2018), Method of Time Series Similarity Measurement Based on Dynamic Time Warping,
Computers, Materials & Continua, 57(1), s.97-106. doi:10.32604/cmc.2018.03511.
- Lucarelli, G., ve Borrotti, M. (2020), A Deep Q-Learning Portfolio Management Framework for the
Cryptocurrency Market, Neural Computing and Applications, 32(23), s.17229-17244.
https://doi.org/10.1007/s00521-020-05359-8.
- Luo, J. (2021), A Study on Stock Graph Recognition Based on Wavelet Denoising and DTW Algorithm,
Mathematical Problems in Engineering, 2021, s.1-15. https://doi.org/10.1155/2021/6641749.
- Markowitz, H. (1952), Portfolio Selection, The Journal of Finance, 7(1), s.77–91. https://doi.org/10.2307/2975974
- Massahi, M., Mahootchi, M., ve Arshadi Khamseh, A. (2020), Development of an Efficient Cluster-Based
Portfolio Optimization Model Under Realistic Market Conditions, Empirical Economics, 59(5), s.2423-2442.
https://doi.org/10.1007/s00181-019-01802-5
- Montenegro, M., ve Albuquerque, P. (2017), Wealth Management: Modeling the Nonlinear Dependence,
Algorithmic Finance, 6(1-2), s.51-65. https://doi.org/10.3233/af-170203
- Nanda, S. R., Mahanty, B., ve Tiwari, M. K. (2010), Clustering Indian Stock Market Data for Portfolio Management,
Expert Systems with Applications, 37(12), s.8793-8798. https://doi.org/10.1016/j.eswa.2010.06.026.
- Nugraha, E. (2024), Portfolio Optimization Analysis Using Markowitz Model on IDX30 Stock Index in 2022 and
2023, Firm Journal of Management Studies, 9(1), 97. https://doi.org/10.33021/firm.v9i1.4990.
- Platanakis, E., ve Urquhart, A. (2020), Should Investors Include Bitcoin in Their Portfolios? a Portfolio Theory
Approach, The British Accounting Review, 52(4), 100837, s.1-19. https://doi.org/10.1016/j.bar.2019.100837.
- Ratanamahatana, C. A. ve Keogh, E. (2004), Making Time-Series Classification More Accurate Using Learned
Constraints, Proceedings of the 2004 SIAM International Conference on Data Mining.
https://doi.org/10.1137/1.9781611972740.2.
- Sakoe, H., ve Chiba, S. (1978), Dynamic Programming Algorithm Optimization for Spoken Word Recognition,
IEEE transactions on acoustics, speech, and signal processing, 26(1), s.43-49.
- Salvador, S., ve Chan, P. (2007), Toward Accurate Dynamic Time Warping in Linear Time and Space, Intelligent
Data Analysis, 11(5), s.561-580. DOI: 10.3233/IDA-2007-11508.
- Shirota, Y., ve Murakami, A. (2021), Long-term Time Series Data Clustering of Stock Prices for Portfolio
Selection, In 2021 IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI) 1-
6.
- Širůček, M., ve Křen, L. (2017), Application of Markowitz Portfolio Theory by Building Optimal Portfolio on the US
Stock Market, J. Stanković, P. Delias, S. Marinković, S. Rochhia (Eds.), In Tools and Techniques for Economic
Decision Analysis (pp. 24-42). IGI Global.
- Tatsat, H., Puri, S., ve Lookabaugh, B. (2020), Machine Learning and Data Science Blueprints for Finance,
O'Reilly media.
- Tayalı, S. T. (2020), A Novel Backtesting Methodology for Clustering in Mean–Variance Portfolio Optimization, Knowledge-Based Systems, 209, s.1-12. https://doi.org/10.1016/j.knosys.2020.106454
- Torre-Torres, O. V. D. l., Figueroa, E. G., ve Montoya, D. A. (2015), An Actual Position Benchmark for Mexican Pension Funds Performance, Economía Teoría Y Práctica, (43). https://doi.org/10.24275/etypuam/ne/432015/delatorre.
- Vaclavik, M., ve Jablonsky, J. (2012) Revisions of Modern Portfolio Theory Optimization Model, Central European
journal of operations research, 20, s.473-483. DOI 10.1007/s10100-011-0227-2.
- Vahidipour, S., Mirzaei, A., ve Rahmati, M. (2014), Comparing Weighted Combination of Hierarchical Clustering
Based on Cophenetic Measure, Intelligent Data Analysis, 18(4), s.547-559. https://doi.org/10.3233/ida-1406,57.
- Wang, Y. (2023), Select the Optimal Portfolio by Analyzing and Comparing the Better Performance of
Markowitz Model and Index Model Under 5 Different Constraints, Advances in Economics, Management and
Political Sciences, 13(1), s.364-376. https://doi.org/10.54254/2754-1169/13/20230753.
- Xu, Y., Zhao, X., Chen, Y., ve Yang, Z. (2019), Research on A Mixed Gas Classification Algorithm Based on
Extreme Random Tree, Applied Sciences, 9(9), 1728, s.1-17. https://doi.org/10.3390/app9091728.