- (1) Clustering for ZR,t. First, by Rohe et al. (2016) and solution of (1 + ε)-approximate k-means clustering, for each period t = 1, , T, we have MR t N ⤠8(2 + ε)2 m2 rN kUt â UtOtk2 F , (20) where mr def = min i,t {min{kÎR,t(i, â)k, kÎR,t(i, â)k}}, (21) and ÎR,t and ÎR,t are defined in Lemma 3.
Paper not yet in RePEc: Add citation now
Abadi, J. and M. Brunnermeier (2018). Blockchain economics. NBER Working Paper 25407. Abbe, E., J. Fan, and K. Wang (2020). An `p theory of PCA and spectral clustering. arXiv preprint arXiv:2006.14062.
Acemoglu, D., A. Ozdaglar, and A. Tahbaz-Salehi (2015). Systemic risk and stability in financial networks. American Economic Review 105(2), 564â608.
Ali, U. and D. Hirshleifer (2020). Shared analyst coverage: unifying momentum spillover effects. Journal of Financial Economics 136(3), 649â675.
- Altman, N. S. (1990). Kernel smoothing of data with correlated errors. Journal of the American Statistical Association 85(411), 749â759.
Paper not yet in RePEc: Add citation now
- Amini, A. A. and E. Levina (2018). On semidefinite relaxations for the block model. Annals of Statistics 46(1), 149â179.
Paper not yet in RePEc: Add citation now
- Amini, A. A., A. Chen, P. J. Bickel, and E. Levina (2013). Pseudo-likelihood methods for community detection in large sparse networks. Annals of Statistics 41(4), 2097â2122.
Paper not yet in RePEc: Add citation now
- Aobdia, D., J. Caskey, and N. B. Ozel (2014). Inter-industry network structure and the crosspredictability of earnings and stock returns. Review of Accounting Studies 19(3), 1191â1224.
Paper not yet in RePEc: Add citation now
Atmaz, A. and S. Basak (2018). Belief dispersion in the stock market. Journal of Finance 73(3), 1225â1279.
Baker, S. R., N. Bloom, and S. J. Davis (2016). Measuring economic policy uncertainty. Quarterly Journal of Economics 131(4), 1593â1636.
Biais, B., C. Bisiere, M. Bouvard, and C. Casamatta (2019). The blockchain folk theorem. Review of Financial Studies 32(5), 1662â1715.
- Bickel, P. J. and A. Chen (2009). A nonparametric view of network models and newmanâgirvan and other modularities. Proceedings of the National Academy of Sciences 106(50), 21068â21073.
Paper not yet in RePEc: Add citation now
- Bickel, P., D. Choi, X. Chang, and H. Zhang (2013). Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels. Annals of Statistics 41(4), 1922â 1943.
Paper not yet in RePEc: Add citation now
Binkiewicz, N., J. T. Vogelstein, and K. Rohe (2017). Covariate-assisted spectral clustering. Biometrika 104(2), 361â377.
Brogaard, J. and A. Detzel (2015). The asset-pricing implications of government economic policy uncertainty. Management Science 61(1), 3â18.
Brunnermeier, M. K. and L. H. Pedersen (2009). Market liquidity and funding liquidity. Review of Financial Studies 22(6), 2201â2238.
Brunnermeier, M. K., S. Nagel, and L. H. Pedersen (2008). Carry trades and currency crashes. NBER Macroeconomics Annual 23(1), 313â348.
Budish, E. (2018). The economic limits of bitcoin and the blockchain. NBER Working Paper 24717.
- Cai, T. T. and X. Li (2015). Robust and computationally feasible community detection in the presence of arbitrary outlier nodes. Annals of Statistics 43(3), 1027â1059.
Paper not yet in RePEc: Add citation now
- Celisse, A., J.-J. Daudin, and L. Pierre (2012). Consistency of maximum-likelihood and variational estimators in the stochastic block model. Electronic Journal of Statistics 6, 1847â1899.
Paper not yet in RePEc: Add citation now
- Chen and Lei (2017) propose a network cross-validation procedure to estimate the number of clusters by utilizing adjacency information. Li, Levina, and Zhu (2020) refine the network crossvalidation approach by proposing an edge sampling algorithm. In our case, we apply the network cross-validation approach directly to the similarity matrix instead of the adjacency matrix. This is because the covariate matrix Cw t behaves just like an adjacency matrix when we use dummy variables to indicate different technology attributes. Therefore, the network cross-validation applies to the similarity matrix in our study. 7 Proof of Main Results 7.1 Proof of Theorem 1 Proof. In this proof, we deal with the clustering of left singular vector and the right singular vectors separately.
Paper not yet in RePEc: Add citation now
Chen, C. Y.-H., W. K. HaÌrdle, and Y. Okhrin (2019). Tail event driven networks of SIFIs. Journal of Econometrics 208(1), 282â298.
- Chen, K. and J. Lei (2017). Network cross-validation for determining the number of communities in network data. Journal of the American Statistical Association, 1â11.
Paper not yet in RePEc: Add citation now
- Chen, Y. and J. Xu (2016). Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices. Journal of Machine Learning Research 17(1), 882â938.
Paper not yet in RePEc: Add citation now
- Chen, Y., J. Fan, C. Ma, and Y. Yan (2019). Inference and uncertainty quantification for noisy matrix completion. Proceedings of the National Academy of Sciences 116(46), 22931â22937.
Paper not yet in RePEc: Add citation now
Cheng, H.-P. and K.-C. Yen (2020). The relationship between the economic policy uncertainty and the cryptocurrency market. Finance Research Letters 35, 101308.
Cohen, L. and A. Frazzini (2008). Economic links and predictable returns. Journal of Fi37 nance 63(4), 1977â2011.
- Cong, L. W., Y. Li, and N. Wang (2021a). Token-based platform finance. Journal of Financial Economics, forthcoming.
Paper not yet in RePEc: Add citation now
- Cong, L. W., Y. Li, and N. Wang (2021b). Tokenomics: dynamic adoption and valuation. Review of Financial Studies 34(3), 1105â1155.
Paper not yet in RePEc: Add citation now
Cong, L. W., Z. He, and J. Li (2021). Decentralized mining in centralized pools. Review of Financial Studies 34(3), 1191â1235.
Daniel, K., D. Hirshleifer, and A. Subrahmanyam (1998). Investor psychology and security market under-and overreactions. Journal of Finance 53(6), 1839â1885.
- Decelle, A., F. Krzakala, C. Moore, and L. ZdeborovaÌ (2011). Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications. Physical Review E 84(6), 066106.
Paper not yet in RePEc: Add citation now
Demir, E., G. Gozgor, C. K. M. Lau, and S. A. Vigne (2018). Does economic policy uncertainty predict the bitcoin returns? An empirical investigation. Finance Research Letters 26, 145â149.
- Deshpande, Y., S. Sen, A. Montanari, and E. Mossel (2018). Contextual stochastic block models. In Advances in Neural Information Processing Systems, Volume 31.
Paper not yet in RePEc: Add citation now
Detzel, A., H. Liu, J. Strauss, G. Zhou, and Y. Zhu (2021). Learning and predictability via technical analysis: evidence from bitcoin and stocks with hard-to-value fundamentals. Financial Management 50(1), 107â137.
Easley, D., M. OâHara, and S. Basu (2019). From mining to markets: the evolution of bitcoin transaction fees. Journal of Financial Economics 134(1), 91â109.
- Esmaeili, M., H. M. Saad, and A. Nosratinia (2021). Semidefinite programming for community detection with side information. IEEE Transactions on Network Science and Engineering.
Paper not yet in RePEc: Add citation now
Fama, E. F. and K. R. French (1993). Common risk factors in stock and bond returns. Journal of Financial Economics 33(1), 3â56.
- Fama, E. F., K. R. French, D. G. Booth, and R. Sinquefield (1993). Differences in the risks and returns of NYSE and NASD stocks. Financial Analysts Journal 49(1), 37â41.
Paper not yet in RePEc: Add citation now
- Fan, J., Y. Fan, X. Han, and J. Lv (2019). SIMPLE: Statistical inference on membership profiles in large networks. arXiv preprint arXiv:1910.01734.
Paper not yet in RePEc: Add citation now
Fan, J., Y. Liao, and M. Mincheva (2013). Large covariance estimation by thresholding principal orthogonal complements. Journal of the Royal Statistical Society. Series B, Statistical methodology 75(4).
- Fanti, G., L. Kogan, and P. Viswanath (2019). Economics of Proof-of-Stake payment systems. Working paper, MIT.
Paper not yet in RePEc: Add citation now
Foerster, S. R. and G. A. Karolyi (1999). The effects of market segmentation and investor recognition on asset prices: evidence from foreign stocks listing in the united states. Journal of Finance 54(3), 981â1013.
- From Lemma 1 and the proofs of the previous theorems, we can see that k b St,r â St,rk is decreasing, while kSt,r â Stk is increasing in r. Therefore, there exists an optimal râ that achieves the best bias-variance balance; that is, râ = arg min 0â¤râ¤T/2 (1 â η)â2 Wmax â d r ⨠1 + kSt,r â Stk ! . (17) Then, we can apply Lepskiâs method (Lepski et al., 1997) to construct the adaptive estimator for râ . Without loss of generality, we choose η = 1/2. The, we define the adaptive estimator as b r = max ( 0 ⤠r ⤠T/2 : b St,r â b St,Ï â¤ 4Wmax s
Paper not yet in RePEc: Add citation now
- Gao, C., Z. Ma, A. Y. Zhang, and H. H. Zhou (2018). Community detection in degree-corrected block models. Annals of Statistics 46(5), 2153â2185.
Paper not yet in RePEc: Add citation now
- Gasser, T. and H.-G. MuÌller (1979). Kernel estimation of regression functions. In Smoothing techniques for curve estimation, pp. 23â68. Springer.
Paper not yet in RePEc: Add citation now
Griffin, J. M. (2002). Are the Fama and French factors global or country specific? The Review of Financial Studies 15(3), 783â803.
Griffin, J. M. and A. Shams (2020). Is Bitcoin really un-Tethered? Journal of Finance 75(4), 1913â1964.
- Guo, L., L. Peng, Y. Tao, and J. Tu (2021). Joint news, attention spillover, and market returns. Available at SSRN 2927561.
Paper not yet in RePEc: Add citation now
- Hajek, B., Y. Wu, and J. Xu (2016a). Achieving exact cluster recovery threshold via semidefinite programming. IEEE Transactions on Information Theory 62(5), 2788â2797.
Paper not yet in RePEc: Add citation now
- Hajek, B., Y. Wu, and J. Xu (2016b). Achieving exact cluster recovery threshold via semidefinite programming: Extensions. IEEE Transactions on Information Theory 62(10), 5918â5937.
Paper not yet in RePEc: Add citation now
Herskovic, B. (2018). Networks in production: asset pricing implications. Journal of Finance 73(4), 1785â1818.
- Hinzen, F. J., K. John, and F. Saleh (2019). Proof-of-Workâs limited adoption problem. Working Paper, NYU Stern School of Business.
Paper not yet in RePEc: Add citation now
Hoberg, G. and G. Phillips (2016). Text-based network industries and endogenous product differentiation.
- Holland, P. W., K. B. Laskey, and S. Leinhardt (1983). Stochastic blockmodels: first steps. Social Networks 5(2), 109â137.
Paper not yet in RePEc: Add citation now
Hong, H. and J. C. Stein (1999). A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance 54(6), 2143â2184.
Hong, H., T. Lim, and J. C. Stein (2000). Bad news travels slowly: Size, analyst coverage, and the profitability of momentum strategies. Journal of Finance 55(1), 265â295.
Hou, K. and T. J. Moskowitz (2005). Market frictions, price delay, and the cross-section of expected returns. Review of Financial Studies 18(3), 981â1020.
- Jin, J. (2015). Fast community detection by score. Annals of Statistics 43(1), 57â89.
Paper not yet in RePEc: Add citation now
- Joseph, A. and B. Yu (2016). Impact of regularization on spectral clustering. Annals of Statistics 44(4), 1765â1791.
Paper not yet in RePEc: Add citation now
- Kan, R. and G. Kirikos (1995). Biases in evaluating trading strategies. Working Paper, University of Toronto.
Paper not yet in RePEc: Add citation now
- Karrer, B. and M. E. J. Newman (2011). Stochastic blockmodels and community structure in networks. Physical Review E 83(1), 016107.
Paper not yet in RePEc: Add citation now
- Kim, A., S. Trimborn, and W. K. HaÌrdle (2019). VCRIX â a volatility index for cryptocurrencies. Available at SSRN 3480348.
Paper not yet in RePEc: Add citation now
Koumou, G. B. (2020). Diversification and portfolio theory: a review. Financial Markets and Portfolio Management 34, 267â312.
Lan, W., Z. Fang, H. Wang, and C.-L. Tsai (2018). Covariance matrix estimation via network structure. Journal of Business & Economic Statistics 36(2), 359â369.
Lee, C. M., S. T. Sun, R. Wang, and R. Zhang (2019). Technological links and predictable returns. Journal of Financial Economics 132(3), 76â96.
- Lei, J. and A. Rinaldo (2015). Consistency of spectral clustering in stochastic block models. Annals of Statistics 43(1), 215â237.
Paper not yet in RePEc: Add citation now
- Lepski, O. V., E. Mammen, and V. G. Spokoiny (1997). Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Annals of Statistics 25(3), 929â947.
Paper not yet in RePEc: Add citation now
Li, T., E. Levina, and J. Zhu (2020). Network cross-validation by edge sampling. Biometrika 107(2), 257â276.
- Li, X., Y. Chen, and J. Xu (2021). Convex relaxation methods for community detection. Statistical Science 36(1), 2â15.
Paper not yet in RePEc: Add citation now
- Liu, J., I. W. Marsh, P. Mazza, and M. Petitjean (2021). Factor structure in cryptocurrency returns and volatility. Available at SSRN 3389152.
Paper not yet in RePEc: Add citation now
Liu, Y. and A. Tsyvinski (2021). Risks and returns of cryptocurrency. Review of Financial Studies 34(6), 2689â2727.
- Liu, Y., A. Tsyvinski, and X. Wu (2021). Common risk factors in cryptocurrency. Journal of Finance, forthcoming.
Paper not yet in RePEc: Add citation now
- Liu, Y., J. Sheng, and W. Wang (2021). Technology and cryptocurrency valuation: evidence from machine learning. Available at SSRN 3577208.
Paper not yet in RePEc: Add citation now
- Lu, C. and S. Sen (2020). Contextual stochastic block model: Sharp thresholds and contiguity.
Paper not yet in RePEc: Add citation now
- Ma, Z. and Z. Ma (2017). Exploration of large networks with covariates via fast and universal latent space model fitting. arXiv preprint arXiv:1705.02372.
Paper not yet in RePEc: Add citation now
Makarov, I. and A. Schoar (2020). Trading and arbitrage in cryptocurrency markets. Journal of Financial Economics 135(2), 293â319.
Markowitz, H. (1952). The utility of wealth. Journal of Political Economy 60(2), 151â158.
Matias, C. and V. Miele (2017). Statistical clustering of temporal networks through a dynamic stochastic block model. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79(4), 1119â1141.
Menzly, L. and O. Ozbas (2010). Market segmentation and cross-predictability of returns. Journal of Finance 65(4), 1555â1580.
Moskowitz, T. J. and M. Grinblatt (1999). Do industries explain momentum? Journal of Finance 54(4), 1249â1290.
- Mu, C., A. Mele, L. Hao, J. Cape, A. Athreya, and C. E. Priebe (2020). On spectral algorithms for community detection in stochastic blockmodel graphs with vertex covariates. arXiv preprint arXiv:2007.02156.
Paper not yet in RePEc: Add citation now
- NkStkâ Ï â¨ 1 , for any Ï < r ) . (18) Next, for the choice of αt, we select αt to achieve a balance between LÏ,t and Cw t : αt = λK(LÏ,t) â λK+1(LÏ,t) λ1(Cw t ) . (19) Lastly, to determine K, we have several choices. Wang and Bickel (2017b) implement a pseudo likelihood approach to choose the number of clusters in a stochastic blockmodel without covariates.
Paper not yet in RePEc: Add citation now
Nowicki, K. and T. A. B. Snijders (2001). Estimation and prediction for stochastic blockstructures.
- Pagnotta, E. (2020). Decentralizing money: Bitcoin prices and blockchain security. Review of Financial Studies, forthcoming.
Paper not yet in RePEc: Add citation now
Parsons, C. A., R. Sabbatucci, and S. Titman (2020). Geographic lead-lag effects. Review of Financial Studies 33(10), 4721â4770.
- Patton, A. J. and B. Weller (2019). Risk price variation: The missing half of empirical asset pricing. Economic Research Initiatives at Duke (ERID) Working Paper (274).
Paper not yet in RePEc: Add citation now
Peng, L. and W. Xiong (2006). Investor attention, overconfidence and category learning. Journal of Financial Economics 80(3), 563â602.
- Pensky, M. and T. Zhang (2019). Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics 13(1), 678â709.
Paper not yet in RePEc: Add citation now
- Qin, T. and K. Rohe (2013). Regularized spectral clustering under the degree-corrected stochastic blockmodel. In Advances in Neural Information Processing Systems, Volume 26, pp. 3120â3128.
Paper not yet in RePEc: Add citation now
- Rohe, K., S. Chatterjee, and B. Yu (2011). Spectral clustering and the high-dimensional stochastic blockmodel. Annals of Statistics 39(4), 1878â1915.
Paper not yet in RePEc: Add citation now
- Rohe, K., T. Qin, and B. Yu (2016). Co-clustering directed graphs to discover asymmetries and directional communities. Proceedings of the National Academy of Sciences 113(45), 12679â12684.
Paper not yet in RePEc: Add citation now
- Roy, A. D. (1952). Safety first and the holding of assets. Econometrica, 431â449.
Paper not yet in RePEc: Add citation now
Rubinstein, M. (2002). Markowitzâs âportfolio selectionâ: a fifty-year retrospective. Journal of Finance 57(3), 1041â1045.
- Saleh, F. (2021). Blockchain without waste: Proof-of-Stake. Review of Financial Studies 34(3), 1156â1190.
Paper not yet in RePEc: Add citation now
- Sharpe, W. F. (1966). Mutual fund performance. Journal of Business 39(1), 119â138.
Paper not yet in RePEc: Add citation now
Shleifer, A. and R. W. Vishny (1997). The limits of arbitrage. Journal of Finance 52(1), 35â55.
Sockin, M. and W. Xiong (2020). A model of cryptocurrencies. NBER Working Paper 26816.
- Wang, Y. R. and P. J. Bickel (2017a). Likelihood-based model selection for stochastic block models. Annals of Statistics 45(2), 500â528.
Paper not yet in RePEc: Add citation now
- Wang, Y. X. R. and P. J. Bickel (2017b). Likelihood-based model selection for stochastic block models. Annals of Statistics 45(2), 500â528.
Paper not yet in RePEc: Add citation now
- Weng, H. and Y. Feng (2016). Community detection with nodal information. arXiv preprint arXiv:1610.09735.
Paper not yet in RePEc: Add citation now
- Yan, B. and P. Sarkar (2020). Covariate regularized community detection in sparse graphs. Journal of the American Statistical Association, 1â12.
Paper not yet in RePEc: Add citation now
Yermack, D. (2017). Corporate governance and blockchains. Review of Finance 21(1), 7â31.
- Zhang, Y., E. Levina, and J. Zhu (2016). Community detection in networks with node features. Electronic Journal of Statistics 10(2), 3153â3178.
Paper not yet in RePEc: Add citation now
- Zhang, Y., M. Poux-Berthe, C. Wells, K. Koc-Michalska, and K. Rohe (2018). Discovering political topics in facebook discussion threads with graph contextualization. Annals of Applied Statistics 12(2), 1096â1123.
Paper not yet in RePEc: Add citation now
- Zhao, J., X. Liu, H. Wang, and C. Leng (2021). Dimension reduction for covariates in network data. Biometrika, forthcoming.
Paper not yet in RePEc: Add citation now
- Zhao, Y., E. Levina, and J. Zhu (2012). Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics 40(4), 2266â2292.
Paper not yet in RePEc: Add citation now
- Zhou, Z. and A. A. Amini (2019). Analysis of spectral clustering algorithms for community detection: the general bipartite setting. Journal of Machine Learning Research 20(1), 1774â1820.
Paper not yet in RePEc: Add citation now
- Zhou, Z. and A. A. Amini (2020). Optimal bipartite network clustering. Journal of Machine Learning Research 21, 1â68.
Paper not yet in RePEc: Add citation now
- Zhu, X., Z. Cai, and Y. Ma (2021). Network functional varying coefficient model. Journal of the American Statistical Association, 1â12.
Paper not yet in RePEc: Add citation now
Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101(476), 1418â1429.
Zou, T., W. Lan, H. Wang, and C.-L. Tsai (2017). Covariance regression analysis. Journal of the American Statistical Association 112(517), 266â281.
- Zou, T., W. Lan, R. Li, and C.-L. Tsai (2021). Inference on covariance-mean regression. Journal of Econometrics.
Paper not yet in RePEc: Add citation now