Comparison Of Vector Autoregressive and Multiresponse Fourier Series for Cryptocurrency Prediction Post-Bitcoin Halving 2024

Dita Amelia, Rizky Dwi Kurnia Rahayu, Bimo Okta Syahputra

Abstract


This study examines cryptocurrency price modeling after the 2024 Bitcoin halving by comparing two multivariate forecasting methods: the Vector Autoregressive (VAR) model and the cosine-based Multiresponse Fourier Series Estimator. The research aligns with SDGs 8 on Decent Work and Economic Growth, as accurate forecasting in digital asset markets can support financial stability and informed investment decisions. The novelty of this study lies in applying a Fourier-based multiresponse model for post-halving cryptocurrency prediction, an approach that remains limited in existing literature. The dataset consists of daily prices of Bitcoin, Ethereum, and Litecoin from April 2024 to August 2025 (t=480), obtained from investing.com, with 90% for data training and 10% for data testing. Prior to modeling, the Bartlett test produced p-value 0.000<α, indicating significant correlations among cryptocurrencies, thereby validating the use of simultaneous multivariate analysis. The results show that the Fourier Series Estimator with five oscillation parameters (k=5) provides superior predictive accuracy, achieving a MAPE of 3.768%, compared to the VAR model’s MAPE of 8.503%. These findings demonstrate that the Fourier estimator more effectively captures cyclical and nonlinear patterns in digital assets and offers valuable contributions to financial statistics, providing practical insights for investors and policymakers in the highly volatile cryptocurrency market.

Keywords


Cryptocurrency, Bitcoin Halving, Vector Autoregressive, Fourier Series Estimator

Full Text:

PDF

References


[1] TripleA. Global Crypto Ownership Reaches 562 Million People in 2024: New Report. Accessed: Sep. 17, 2025. 2024. https://www.triple-a.io/blog/crypto-ownership-report.

[2] B. Kurylo. “From Dollarization to Bitcoinization: El Salvador’s Monetary Experiment”. In: Latin American Policy 16.2 (June 2025). doi: 10.1111/lamp.70011.

[3] S. Erdogan, M. Y. Ahmed, and S. A. Sarkodie. “Analyzing asymmetric effects of cryptocurrency demand on environmental sustainability”. In: Environmental Science and Pollution Research 29.21 (May 2022), pp. 31723–31733. doi: 10.1007/s11356-021-17998-y.

[4] B. Mutanda and B. C. Nomlala. “Cryptocurrency integration: A blessing or a curse for economic development and stability?” In: Economics, Management and Sustainability 10.1 (June 2025), pp. 127–146. doi: 10.14254/jems.2025.10-1.9.

[5] P.-S. Ko and K.-S. Chen. “Discovering AI tokens in the Fractal Markets Hypothesis and their time-frequency co-movements with the leading high-carbon cryptocurrency”. In: Data Science in Finance and Economics 5.3 (2025), pp. 293–319. doi: 10.3934/DSFE.2025013.

[6] R. Andleeb and A. Hassan. “Impact of Investor Sentiment on Contemporaneous and Future Equity Returns in Emerging Markets”. In: SAGE Open 13.3 (July 2023). doi: 10.1177/21582440231193568.

[7] D. Cho et al. “Bitcoin Halving Events: Historical Analysis and Strategic Insights for Miners”. In: Lecture Notes in Computer Science. Singapore: Springer, 2025, pp. 38–54. doi: 10.1007/978-981-96-4442-1_3.

[8] S. Hansun, A. Wicaksana, and A. Q. M. Khaliq. “Multivariate cryptocurrency prediction: comparative analysis of three recurrent neural networks approaches”. In: Journal of Big Data 9.1 (Dec. 2022), p. 50. doi: 10.1186/s40537-022-00601-7.

[9] R. Amirzadeh et al. “Dynamic Bayesian Networks for Predicting Cryptocurrency Price Directions: Uncovering Causal Relationships”. In: Annals of Data Science (Aug. 2025). doi: 10.1007/s40745-025-00637-5.

[10] S. Sathyanarayana and Sudhindra Gargesa. “Modeling Cryptocurrency (Bitcoin) using Vector Autoregressive (VAR) Model”. In: SDMIMD Journal of Management (Sept. 2019). doi: 10.18311/sdmimd/2019/23181.

[11] M. Düker et al. “Vector AutoRegressive Moving Average Models: A Review”. In: WIREs Computational Statistics 17.1 (Mar. 2025). doi: 10.1002/wics.70009.

[12] Noam Koren and Kira Radinsky. Interpretable Multivariate Time Series Forecasting Using Neural Fourier Transform. 2024. arXiv: 2405.13812 [cs.LG]. https://arxiv.org/abs/2405.13812.

[13] Junxian Zhou, Shoujin Wang, and Yuming Ou. “Fourier Graph Convolution Transformer for Financial Multivariate Time Series Forecasting”. In: 2024 International Joint Conference on Neural Networks (IJCNN). 2024, pp. 1–8. doi: 10.1109/IJCNN60899.2024.10650090.

[14] S. Tobias and J. E. Carlson. “Bartlett’s Test of Sphericity and Chance Findings in Factor Analysis”. In: Multivariate Behavioral Research 4.3 (July 1969), pp. 375–377. doi: 10.1207/s15327906mbr0403_8.

[15] G. Osei and L. Gao. “Utilizing Google Trends Data for Effective Modeling of COVID-19 Outcomes: A Vector Auto Regression (VAR) Approach”. Accessed: Oct. 11, 2025. MA thesis. University of Tennessee at Chattanooga, 2024. https://scholar.utc.edu/theses/809.

[16] H. Lütkepohl. “Structural vector autoregressive analysis for cointegrated variables”. In: Allgemeines Statistisches Archiv 90.1 (Mar. 2006), pp. 75–88. doi: 10.1007/s10182-006-0222-4.

[17] W. Enders. Applied Econometric Time Series. Wiley, 2015.

[18] P. K. Agrawal et al. “Volatility Integration and Dynamic Connectedness Among the Indian Stock Market, Gold Prices, Oil Prices, Exchange Rates and Natural Gas”. In: Economics 13.2 (June 2025), pp. 245–263. doi: 10.2478/eoik-2025-0039.

[19] N. P. A. M. Mariati, I. N. Budiantara, and V. Ratnasari. “The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression”. In: Symmetry (Basel) 13.11 (Nov. 2021), p. 2094. doi: 10.3390/sym13112094.

[20] T. Agustini et al. “Fourier Series Estimator For Estimation of Birespon Nonparametric Regression Curves”. In: International Journal of Technology and Education Research 2.03 (Sept. 2024), pp. 184–212. doi: 10.63922/ijeter.v2i03.1320.

[21] R. Brigola. Fourier Analysis and Distributions: A First Course with Applications. Springer, 2025.

[22] A. Chatterjee and T. Bandyopadhyay. “Regression Models for Group Testing: Identifiability and Asymptotics”. In: Journal of Statistical Planning and Inference 204 (Jan. 2020), pp. 141–152. doi: 10.1016/j.jspi.2019.05.003.

[23] M. Zulfadhli, I. N. Budiantara, and V. Ratnasari. “Nonparametric Regression Estimator of Multivariable Fourier Series for Categorical Data”. In: MethodsX 13 (Dec. 2024), p. 102983. doi: 10.1016/j.mex.2024.102983.

[24] L. Ni’matuzzahroh and A. T. R. Dani. “Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023”. In: Inferensi 7.2 (July 2024), p. 73. doi: 10.12962/j27213862.v7i2.20219.

[25] Suliyanto et al. “Statistical Inferences and Applications of Nonparametric Regression Models Based on Fourier Series”. In: MethodsX 14 (June 2025), p. 103217. doi: 10.1016/j.mex.2025.103217.

[26] P. K. Wardani, I. N. Budiantara, and S. Setiawan. “Selecting Optimal Knot Points and Oscillation Parameters Using Generalized Cross-validation and Unbiased Risk Method in Nonparametric Regression of Combined Spline Truncated and Fourier Series”. In: KnE Social Sciences. Vol. 10. 11. May 2025, pp. 220–234. doi: 10.18502/kss.v10i11.18744.

[27] J. Montaño Moreno et al. “Using the R-MAPE Index as a Resistant Measure of Forecast Accuracy”. In: Psicothema 25.4 (Nov. 2013), pp. 500–506. doi: 10.7334/psicothema2013.23.

[28] Yacouba Boubacar Mainassara. “Tests portmanteau multivariés d’adéquation de modèles VARMA faibles”. In: Comptes Rendus Mathematique 348.15–16 (2010), pp. 927–929. doi: 10.1016/j.crma.2010.07.017.

[29] Peihua Li and Wei Biao Wu. “Rank-based portmanteau tests for serial correlation”. In: Journal of Econometrics (2012). doi: 10.1016/S0047259X12002801.

[30] Juan Carlos Escanciano, Ignacio N. Lobato, and Lin Zhu. “Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models”. In: Journal of Business & Economic Statistics 31.4 (2013), pp. 426–437. doi: 10.1080/07350015.2013.803973.

[31] Ruth Poole et al. “Coffee consumption and health: umbrella review of meta-analyses of multiple health outcomes”. In: Obesity Reviews 19.5 (2018), pp. 641–660. doi: 10.1111/obes.12238.




DOI: https://doi.org/10.18860/cauchy.v11i1.37720

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Dita Amelia, Rizky Dwi Kurnia Rahayu, Bimo Okta Syahputra

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.