Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index
Open accessAbstract
This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model.
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ARIMA can be combined with another algorithm, symmetric generalized autoregressive conditional heteroskedasticity (SGARCH), to improve forecasting performance.
“ARIMA can be combined with another algorithm, symmetric generalized autoregressive conditional heteroskedasticity (SGARCH), to improve forecasting performance.”
From Forecasting Stock Market Prices Using Machine Learning and Deep Learning Models: A Systematic Review, Performance Analysis and Discussion of Implications (2023) · cites this paper as Vo and Ślepaczuk 2022
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Cites
Generalized autoregressive conditional heteroskedasticity
Bollerslev, T. (1986) · Journal of Econometrics · doi:10.1016/0304-4076(86)90063-1 · Cited by 22,346 · see citing works
Engle, R. F. (1982) · Econometrica · doi:10.2307/1912773 · Cited by 20,795 · see citing works
Conditional Heteroskedasticity in Asset Returns: A New Approach
Nelson, D. B. (1991) · Econometrica · doi:10.2307/2938260 · Cited by 10,278 · see citing works
On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993) · The Journal of Finance · doi:10.1111/j.1540-6261.1993.tb05128.x · Cited by 9,047 · see citing works
The Variation of Certain Speculative Prices
Mandelbrot, B. B. (1963) · The Journal of Business · doi:10.1086/294632 · Cited by 4,829 · see citing works
Bollerslev, T., Chou, R. Y., & Kroner, K. F. (1992) · Journal of Econometrics · doi:10.1016/0304-4076(92)90064-x · Cited by 4,313 · see citing works
Introductory Econometrics for Finance
Brooks, C. (2008) · Cambridge University Press eBooks · doi:10.1017/9781108524872 · Cited by 3,705 · see citing works
A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return
Bollerslev, T. (1987) · The Review of Economics and Statistics · doi:10.2307/1925546 · Cited by 2,568 · see citing works
GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics
Engle, R. F. (2001) · The Journal of Economic Perspectives · doi:10.1257/jep.15.4.157 · Cited by 1,225 · see citing works
Stock Price Prediction Using the ARIMA Model
Adebiyi, A. A., Adewumi, A. O., & Ayo, C. K. (2014) · UKSim International Conference on Computer Modelling and Simulation (UKSim) · doi:10.1109/uksim.2014.67 · Cited by 1,169 · see citing works
Time Series Analysis and Its Applications
Shumway, R. H., & Stoffer, D. S. (2000) · Springer Texts in Statistics · doi:10.1007/978-1-4757-3261-0 · Cited by 1,039 · see citing works
Sentana, E. (1995) · The Review of Economic Studies · doi:10.2307/2298081 · Cited by 560 · see citing works
Asset pricing with a factor-arch covariance structure
Engle, R. F., Ng, V. K., & Rothschild, M. (1990) · Journal of Econometrics · doi:10.1016/0304-4076(90)90099-f · Cited by 544 · see citing works
A Class of Nonlinear Arch Models
Higgins, M., & Bera, A. K. (1992) · International Economic Review · doi:10.2307/2526988 · Cited by 412 · see citing works
Weiss, A. A. (1984) · Journal of Time Series Analysis · doi:10.1111/j.1467-9892.1984.tb00382.x · Cited by 282 · see citing works
Garch forecasting performance under different distribution assumptions
Wilhelmsson, A. (2006) · Journal of Forecasting · doi:10.1002/for.1009 · Cited by 122 · see citing works
Batrancea, L. M. (2021) · Mathematics · doi:10.3390/math9060630 · Cited by 62 · see citing works
Momentum and contrarian effects on the cryptocurrency market
Kość, K., Sakowski, P., & Ślepaczuk, R. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.02.057 · Cited by 57 · see citing works
Self-citationApplying Hurst Exponent in pair trading strategies on Nasdaq 100 index
Bui, Q., & Ślepaczuk, R. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126784 · Cited by 56 · see citing works
Self-citationGhani, I. M. M., & Rahim, H. A. (2019) · IOP Conference Series Materials Science and Engineering · doi:10.1088/1757-899x/548/1/012023 · Cited by 43 · see citing works
LSTM in Algorithmic Investment Strategies on BTC and S&P500 Index
Michańków, J., Sakowski, P., & Ślepaczuk, R. (2022) · Sensors · doi:10.3390/s22030917 · Cited by 36 · see citing works
Self-citationModelling and forecasting S&P 500 stock prices using hybrid Arima-Garch Model
Mustapa, F. H., & Ismail, M. T. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1366/1/012130 · Cited by 36 · see citing works
Robustness of Support Vector Machines in Algorithmic Trading on Cryptocurrency Market
Ślepaczuk, R., & Zenkova, M. (2018) · Central European Economic Journal · doi:10.1515/ceej-2018-0022 · Cited by 30 · see citing works
Self-citationThe performance of hybrid ARIMA-GARCH modeling in forecasting gold price
(2013) · International Congress on Modelling and Simulation (MODSIM) · doi:10.36334/modsim.2013.f2.yaziz · Cited by 28 · see citing works
Hauser, M., & Kunst, R. M. (1998) · Review of Quantitative Finance and Accounting · doi:10.1023/a:1008252331292 · Cited by 27 · see citing works
Modeling and Predicting Stock Market Returns: A Case Study on Dhaka Stock Exchange of Bangladesh
Kamruzzaman, M., Khudri, M. M., & Rahman, M. M. (2017) · Dhaka University Journal of Science · doi:10.3329/dujs.v65i2.54515 · Cited by 17 · see citing works
Information flows and stock market volatility
Chua, C. L., & Tsiaplias, S. (2018) · Journal of Applied Econometrics · doi:10.1002/jae.2649 · Cited by 16 · see citing works
Formulating the Concept of an Investment Strategy Adaptable to Changes in the Market Situation
Ivanyuk, V. A. (2021) · Economies · doi:10.3390/economies9030095 · Cited by 13 · see citing works
Predicting prices of S&P500 index using classical methods and recurrent neural networksPreprint
Kijewski, M., & Ślepaczuk, R. (2020) · RePEc: Research Papers in Economics · Cited by 13 · see citing works
Self-citationChlebuś, M., Dyczko, M., & Woźniak, M. (2021) · Central European Economic Journal · doi:10.2478/ceej-2021-0004 · Cited by 12 · see citing works
Jabłecki, J., Kokoszczyński, R., Sakowski, P., Ślepaczuk, R., & Wójcik, P. T. (2015) · Peter Lang D eBooks · doi:10.3726/978-3-653-04787-5 · Cited by 12 · see citing works
Self-citationEnhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models
la Torre-Torres, O. V. D., Venegas-Martı́nez, F., & Martínez-Torre-Enciso, M. I. (2021) · Mathematics · doi:10.3390/math9020185 · Cited by 11 · see citing works
Equity Return Modeling and Prediction Using Hybrid ARIMA-GARCH Model
Sun, K. (2017) · International Journal of Financial Research · doi:10.5430/ijfr.v8n3p154 · Cited by 10 · see citing works
Guobužaitė, R., & Teresienė, D. (2021) · Economies · doi:10.3390/economies9020086 · Cited by 7 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- [15]Tsay R.S. An Introduction to Analysis of Financial Data with R John Wiley & Sons Street Hoboken, NJ, USA 2012
- [36]Allison P.D. Multiple Regression: A Primer Pine Forge Press Thousand Oaks, CA, USA 1999
Cited by
Sorted by citations
Sonkavde, G., Dharrao, D. S., Bongale, A. M., Deokate, S. T., Doreswamy, D., & Bhat, S. K. (2023) · International Journal of Financial Studies · doi:10.3390/ijfs11030094 · Cited by 262 · see citing works
“These methods were very well adopted before the success of deep learning models.”
MethodSun, K., He, W., Shen, Y., Yan, T., Liu, C., Yang, Z., Han, J., & Xie, W. (2023) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2023.161561 · Cited by 52 · see citing works
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Fang, W., Zhang, S., & Xu, C. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.121968 · Cited by 46 · see citing works
LSTM-ARIMA as a hybrid approach in algorithmic investment strategies
Kashif, K., & Ślepaczuk, R. (2025) · Knowledge-Based Systems · doi:10.1016/j.knosys.2025.113563 · Cited by 45 · see citing works
Self-citationGao, X., Zang, Y., Ma, Q., Liu, M., Cui, Y., & Dang, D.-Z. (2025) · Energy · doi:10.1016/j.energy.2025.136220 · Cited by 39 · see citing works
A hybrid model for stock price prediction based on multi-view heterogeneous data
Long, W., Gao, J., Bai, K., & Lu, Z. (2024) · Financial Innovation · doi:10.1186/s40854-023-00519-w · Cited by 38 · see citing works
LSTM in Algorithmic Investment Strategies on BTC and S&P500 Index
Michańków, J., Sakowski, P., & Ślepaczuk, R. (2022) · Sensors · doi:10.3390/s22030917 · Cited by 36 · see citing works
Self-citationModeling and Forecasting Somali Economic Growth Using ARIMA Models
Mohamed, A. O. (2022) · Forecasting · doi:10.3390/forecast4040056 · Cited by 32 · see citing works
Evaluation Standards of Intelligent Technology based on Financial Alternative Data
Lv, Z., Wang, N., Ma, X., Sun, Y., Meng, Y., & Tian, Y. (2022) · Journal of Innovation & Knowledge · doi:10.1016/j.jik.2022.100229 · Cited by 30 · see citing works
Michańków, J., Sakowski, P., & Ślepaczuk, R. (2024) · Journal of Computational Science · doi:10.1016/j.jocs.2024.102375 · Cited by 27 · see citing works
Self-citationPrediction of stock return by LSTM neural network
Qiao, R., Chen, W., & Qiao, Y. (2022) · Applied Artificial Intelligence · doi:10.1080/08839514.2022.2151159 · Cited by 23 · see citing works
Optimal Markowitz portfolio using returns forecasted with time series and machine learning models
Ślusarczyk, D., & Ślepaczuk, R. (2025) · Journal Of Big Data · doi:10.1186/s40537-025-01164-z · Cited by 22 · see citing works
Self-citationBehera, J., & Kumar, P. (2025) · Applied Soft Computing · doi:10.1016/j.asoc.2025.112741 · Cited by 20 · see citing works
Xing, Y., Yan, C., & Xie, C. C. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-85856-7_34 · Cited by 14 · see citing works
Li, X., Li, S., Zhou, P., & Chen, G. (2022) · Entropy · doi:10.3390/e24040478 · Cited by 13 · see citing works
Ziółkowski, K., & Wieczyński, P. (2025) · Quality & Quantity · doi:10.1007/s11135-025-02325-1 · Cited by 6 · see citing works
A neural network informer in algorithmic investment strategies on high-frequency bitcoin data
Stefaniuk, F., & Ślepaczuk, R. (2026) · Expert Systems with Applications · doi:10.1016/j.eswa.2026.131599 · Cited by 5 · see citing works
Self-citationOn a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading
Azhmyakov, V., Shirokov, I., Dernov, Y., & Trujillo, L. A. G. (2023) · Journal of risk and financial management · doi:10.3390/jrfm16090387 · Cited by 5 · see citing works
Özçalıcı, M., & Kaya, E. (2025) · Spectrum of Decision Making and Applications. · doi:10.31181/sdmap21202519 · Cited by 4 · see citing works
Kayit, A. D., & Tahir, M. I. (2024) · Journal of the Nigerian Society of Physical Sciences · doi:10.46481/jnsps.2024.2039 · Cited by 3 · see citing works
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Петков, П., Шопова, М., Varbanov, T., Ovchinnikov, E., & Лалев, А. (2024) · Journal of risk and financial management · doi:10.3390/jrfm17080346 · Cited by 3 · see citing works
Ullah, R., Jan, M. N., & Tahir, M. (2025) · Future Business Journal · doi:10.1186/s43093-025-00560-4 · Cited by 3 · see citing works
Accurate and efficient stock market index prediction: an integrated approach based on VMD-SNNs
Chen, X., Tang, G., Ren, Y., Lin, X., & Li, T. (2024) · Journal of Applied Statistics · doi:10.1080/02664763.2024.2395961 · Cited by 3 · see citing works
Michańków, J., Sakowski, P., & Ślepaczuk, R. (2024) · Proceedings of the International Conference on Information Systems Development · doi:10.62036/isd.2024.57 · Cited by 2 · see citing works
Self-citationRoshanpour, R., Parsanejad, M., & Pishvaee, M. S. (2026) · IEEE Access · doi:10.1109/access.2026.3662286 · Cited by 2 · see citing works
Improving Prediction of Bursa Malaysia Stock Index Using Time Series and Deep Learning Hybrid Model
Shakawi, A. M. H. A., & Shabri, A. (2024) · Lecture notes on data engineering and communications technologies · doi:10.1007/978-3-031-59711-4_11 · Cited by 2 · see citing works
Long-Term Forecasting of Euro-Dollar Exchange Rates Using the ARIMA Model and Multilayer Perceptron
Chasipanta, G. R. V., & Sánchez-Pozo, N. N. (2024) · Ingénierie des systèmes d information · doi:10.18280/isi.290114 · Cited by 2 · see citing works
Wu, Q., Lu, J., & Zhang, H. (2023) · Highlights in Business Economics and Management · doi:10.54097/hbem.v10i.8043 · Cited by 1 · see citing works
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Chadha, R. S., Jugesh, Parveen, S., & Singh, J. (2023) · Journal of Soft Computing Paradigm · doi:10.36548/jscp.2023.3.007 · Cited by 1 · see citing works
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Metghalchi, M., Cloninger, P. A., & Niroomand, F. (2023) · International Journal of Financial Engineering · doi:10.1142/s2424786323500330 · Cited by 1 · see citing works
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Li, Q., Wen, Y., Yan, Z., & Zeng, F. (2023) · IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C) · doi:10.1109/qrs-c60940.2023.00050 · Cited by 1 · see citing works
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Wei, B., Chen, J., Jiang, P., & Xiao, Z. (2024) · International Conference on Neuromorphic Computing (ICNC) · doi:10.1109/icnc64304.2024.10987665 · Cited by 1 · see citing works
Liu, B. (2023) · Highlights in Business Economics and Management · doi:10.54097/hbem.v10i.8111
Zhou, Y. (2024) · International Journal of Information System Modeling and Design · doi:10.4018/ijismd.364102
Dependent and Independent Time Series Errors Under Elliptically Countered Models
Ramírez, F. O. P., Caro-Lopera, F. J., Díaz-García, J. A., & González-Farı́as, G. (2025) · Econometrics · doi:10.3390/econometrics13020022
Wen, W., Zhang, K., Ma, X., Tao, Y., Liu, X., Deng, Z., & Shen, L. (2026) · Environmental Research Communications · doi:10.1088/2515-7620/ae6397
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Panigrahi, S., Omran, M., & Manaf, M. (2026) · Advances in Science, Technology & Innovation/Advances in science, technology & innovation · doi:10.1007/978-3-032-24784-1_20
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Grobys, K. (2026) · Journal of Forecasting · doi:10.1002/for.70220
- Authors
- Vo, N., & Ślepaczuk, R.
- Affiliations
- University of Warsaw (PL)
- Corresponding author
- Ślepaczuk, Robert
- ORCID
- Ślepaczuk, Robert
- Venue
- Entropy
- Publisher
- MDPI AG
- Published
- 2022-01-20
- Volume
- 24
- Issue
- 2
- Pages
- 158
- ISSN
- 1099-4300 (ISSN-L)
- PMC
- PMC8870867
- OpenAlex
- W4205861619
- Cited by
- 39
- References
- 34
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 10 · 2023: 9 · 2022: 5
- FWCI
- 5.05
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Entropy (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- ReIn UW (University of Warsaw) (submittedVersion, cc-by-nc-nd)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Stock Market Forecasting Methods
- Social Sciences › Economics, Econometrics and Finance › Finance › Financial Risk and Volatility Modeling
- Social Sciences › Economics, Econometrics and Finance › Finance › Financial Markets and Investment Strategies
- Keywords
- S&P 500, algorithmic trading strategies, rolling window forecasting, buy-and-hold benchmark, forecast accuracy, information ratio, maximum drawdown, volatility modeling
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