Abstract
In this paper, we study the possibility of inferring early warning indicators (EWIs) for periods of extreme bitcoin price volatility using features obtained from Bitcoin daily transaction graphs. We infer the low-dimensional representations of transaction graphs in the time period from 2012 to 2017 using Bitcoin blockchain, and demonstrate how these representations can be used to predict extreme price volatility events. Our EWI, which is obtained with a non-negative decomposition, contains more predictive information than those obtained with singular value decomposition or scalar value of the total Bitcoin transaction volume.
N. Antulov-Fantulin and D. Tolic—Shared first authorship.
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Acknowledgement and Contribution
Thanks to students Grüner Maximilian, Weingart Nino, Riesenkampf Heiki for help in processing blockchain data. The work of N.A.F. has been funded by the EU Horizon 2020 SoBigData project under grant agreement No. 654024. All authors contributed to the writing and editing of the manuscript. N.A.F. performed computational modeling and experiments. D.T. performed computational modeling and design of research. M.P. and Z.C. were involved in data processing and analysis. I.V. was involved in financial analysis and interpretation of results.
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In order to solve the following non-convex optimization problem \( {\underset{\mathbf{H,W } \ge 0}{\text {min}}} ||\mathbf X -\mathbf WH ||_{2,1} + \lambda ||\mathbf H ||_{2,1}\) where \(||.||_{2,1}\) denotes the \(L_{2,1}\) matrix norm. First we randomly initialize the matrices \(\mathbf H,W \) then iteratively fix one of the matrices (W,H) and perform the update step on another matrix. The procedure is repeated until the convergence. We use the following updates [34]: \(\mathbf H _{k,i} = \mathbf H _{k,i} \frac{(\mathbf W ^T \mathbf X \mathbf D _1)_{k,i}}{ (\mathbf W ^T \mathbf W \mathbf H \mathbf D _1 + \lambda \mathbf H D _2)_{k,i}}\), \( \mathbf W _{j,k} = \mathbf W _{j,k} \frac{(\mathbf X D _1 \mathbf H ^T)_{j,k}}{ ( \mathbf W H D _1 \mathbf H ^T )_{j,k}}\), where \(\mathbf D _1, \mathbf D _2\) are diagonal matrices defined as: \((\mathbf D _{i,i})_1 = 1 / \sqrt{\sum _j (\mathbf X -\mathbf WH )^2_{j,i}}\) , \((\mathbf D _{i,i})_2 = 1 / \sqrt{\sum _j \mathbf H ^2_{j,i}}.\)
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Antulov-Fantulin, N., Tolic, D., Piskorec, M., Ce, Z., Vodenska, I. (2019). Inferring Short-Term Volatility Indicators from the Bitcoin Blockchain. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 813. Springer, Cham. https://doi.org/10.1007/978-3-030-05414-4_41
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DOI: https://doi.org/10.1007/978-3-030-05414-4_41
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