Lasso-driven inference in time and space. (English) Zbl 1475.62208
Summary: We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the \(Z\)-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.
MSC:
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 60G46 | Martingales and classical analysis |
Keywords:
Bahadur representation; martingale decomposition; simultaneous inference; system of equations; time series; Z-estimation; LassoSoftware:
hdiReferences:
| [1] | Andrews, D. W. K. (1984). Nonstrong mixing autoregressive processes. J. Appl. Probab. 21 930-934. · Zbl 0552.60049 · doi:10.2307/3213710 |
| [2] | Antweiler, W. and Frank, M. Z. (2004). Is all that talk just noise? The information content of Internet stock message boards. J. Finance 59 1259-1294. |
| [3] | Audrino, F. and Tetereva, A. (2019). Sentiment spillover effects for us and European companies. J. Bank. Financ. 106 542-567. |
| [4] | Baker, M. and Wurgler, J. (2006). Investor sentiment and the cross-section of stock returns. J. Finance 61 1645-1680. |
| [5] | Basu, S. and Michailidis, G. (2015). Regularized estimation in sparse high-dimensional time series models. Ann. Statist. 43 1535-1567. · Zbl 1317.62067 · doi:10.1214/15-AOS1315 |
| [6] | Belloni, A., Chen, M. and Chernozhukov, V. (2016). Quantile graphical models: Prediction and conditional independence with applications to financial risk management. Preprint. Available at arXiv:1607.00286. |
| [7] | Belloni, A. and Chernozhukov, V. (2013). Least squares after model selection in high-dimensional sparse models. Bernoulli 19 521-547. · Zbl 1456.62066 · doi:10.3150/11-BEJ410 |
| [8] | Belloni, A., Chernozhukov, V. and Hansen, C. (2011). Inference for high-dimensional sparse econometric models. Preprint. Available at arXiv:1201.0220. · Zbl 1209.62064 |
| [9] | Belloni, A., Chernozhukov, V. and Hansen, C. (2014). Inference on treatment effects after selection among high-dimensional controls. Rev. Econ. Stud. 81 608-650. · Zbl 1409.62142 · doi:10.1093/restud/rdt044 |
| [10] | Belloni, A., Chernozhukov, V. and Kato, K. (2015a). Supplement material for “Uniform post selection inference for least absolute deviation regression and other \(Z\)-estimation problems.” Available at Biometrika online. · Zbl 1345.62049 |
| [11] | Belloni, A., Chernozhukov, V. and Kato, K. (2015b). Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems. Biometrika 102 77-94. · Zbl 1345.62049 · doi:10.1093/biomet/asu056 |
| [12] | Bickel, P. J., Ritov, Y. and Tsybakov, A. B. (2009). Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37 1705-1732. · Zbl 1173.62022 · doi:10.1214/08-AOS620 |
| [13] | Chen, C. Y.-H., Härdle, W. K. and Okhrin, Y. (2019). Tail event driven networks of SIFIs. J. Econometrics 208 282-298. · Zbl 1452.62749 · doi:10.1016/j.jeconom.2018.09.016 |
| [14] | Chernozhukov, V., Chetverikov, D. and Kato, K. (2013). Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors. Ann. Statist. 41 2786-2819. · Zbl 1292.62030 · doi:10.1214/13-AOS1161 |
| [15] | Chernozhukov, V., Chetverikov, D. and Kato, K. (2014). Gaussian approximation of suprema of empirical processes. Ann. Statist. 42 1564-1597. · Zbl 1317.60038 · doi:10.1214/14-AOS1230 |
| [16] | Chernozhukov, V., Chetverikov, D. and Kato, K. (2019). Inference on causal and structural parameters using many moment inequalities. Rev. Econ. Stud. 86 1867-1900. · Zbl 07613855 · doi:10.1093/restud/rdy065 |
| [17] | Chernozhukov, V. and Hansen, C. (2008). Instrumental variable quantile regression: A robust inference approach. J. Econometrics 142 379-398. · Zbl 1418.62154 · doi:10.1016/j.jeconom.2007.06.005 |
| [18] | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. Econom. J. 21 C1-C68. · Zbl 07565928 · doi:10.1111/ectj.12097 |
| [19] | Chernozhukov, V., Karl Härdle, W., Huang, C. and Wang, W. (2021). Supplement to “LASSO-driven inference in time and space.” https://doi.org/10.1214/20-AOS2019SUPP. |
| [20] | Dezeure, R., Bühlmann, P. and Zhang, C.-H. (2017). High-dimensional simultaneous inference with the bootstrap. TEST 26 685-719. · Zbl 06833591 · doi:10.1007/s11749-017-0554-2 |
| [21] | Dimitrakopoulou, K., Tsimpouris, C., Papadopoulos, G., Pommerenke, C., Wilk, E., Sgarbas, K. N., Schughart, K. and Bezerianos, A. (2011). Dynamic gene network reconstruction from gene expression data in mice after influenza A (H1N1) infection. J. Clin. Bioinformat. 1 27. · doi:10.1186/2043-9113-1-27 |
| [22] | Epskamp, S., Waldorp, L. J., Mõttus, R. and Borsboom, D. (2018). The Gaussian graphical model in cross-sectional and time-series data. Multivar. Behav. Res. 53 453-480. · doi:10.1080/00273171.2018.1454823 |
| [23] | Garman, M. B. and Klass, M. J. (1980). On the estimation of security price volatilities from historical data. J. Bus. 53 67-78. |
| [24] | Härdle, W. K., Wang, W. and Yu, L. (2016). TENET: Tail-Event driven NETwork risk. J. Econometrics 192 499-513. · Zbl 1420.62443 · doi:10.1016/j.jeconom.2016.02.013 |
| [25] | Härdle, W. K., Chen, S., Liang, C. and Schienle, M. (2018). Time-varying limit order book networks. IRTG 1792 Discussion Paper 2018-016, IRTG 1792, Humboldt Universität zu Berlin, Germany. |
| [26] | Hautsch, N., Schaumburg, J. and Schienle, M. (2015). Financial network systemic risk contributions. Review of Finance 19 685-738. · Zbl 1417.91560 |
| [27] | Hu, M. and Liu, B. (2004). Mining and summarizing customer reviews. In Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 168-177. |
| [28] | Huang, D., Yin, J., Shi, T. and Wang, H. (2016). A statistical model for social network labeling. J. Bus. Econom. Statist. 34 368-374. · doi:10.1080/07350015.2015.1039014 |
| [29] | Javanmard, A. and Montanari, A. (2014). Hypothesis testing in high-dimensional regression under the Gaussian random design model: Asymptotic theory. IEEE Trans. Inf. Theory 60 6522-6554. · Zbl 1360.62074 · doi:10.1109/TIT.2014.2343629 |
| [30] | Kock, A. B. and Callot, L. (2015). Oracle inequalities for high dimensional vector autoregressions. J. Econometrics 186 325-344. · Zbl 1331.62348 · doi:10.1016/j.jeconom.2015.02.013 |
| [31] | Kolaczyk, E. D. and Csárdi, G. (2014). Statistical Analysis of Network Data with R. Use R! Springer, New York. · Zbl 1290.62002 · doi:10.1007/978-1-4939-0983-4 |
| [32] | Kosorok, M. R. (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer Series in Statistics. Springer, New York. · Zbl 1180.62137 · doi:10.1007/978-0-387-74978-5 |
| [33] | Krampe, J. Kreiss, J.-P. and Paparoditis, E. (2018). Bootstrap based inference for sparse high-dimensional time series models. Preprint. Available at arXiv:1806.11083. · Zbl 1476.62186 |
| [34] | Lahiri, S. N. (1999). Theoretical comparisons of block bootstrap methods. Ann. Statist. 27 386-404. · Zbl 0945.62049 · doi:10.1214/aos/1018031117 |
| [35] | Lin, J. and Michailidis, G. (2017). Regularized estimation and testing for high-dimensional multi-block vector-autoregressive models. J. Mach. Learn. Res. 18 Paper No. 117, 49. · Zbl 1442.62122 · doi:10.1631/jzus.a1500279 |
| [36] | Loughran, T. and McDonald, B. (2011). When is a liability not a liability? Textual analysis, dictionaries, and 10-Ks. J. Finance 66 35-65. |
| [37] | Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer, Berlin. · Zbl 1072.62075 · doi:10.1007/978-3-540-27752-1 |
| [38] | Manresa, E. (2013). Estimating the structure of social interactions using panel data. CEMFI, Madrid. Unpublished manuscript. |
| [39] | Meinshausen, N. and Bühlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436-1462. · Zbl 1113.62082 · doi:10.1214/009053606000000281 |
| [40] | Neykov, M., Ning, Y., Liu, J. S. and Liu, H. (2018). A unified theory of confidence regions and testing for high-dimensional estimating equations. Statist. Sci. 33 427-443. · Zbl 1403.62101 · doi:10.1214/18-STS661 |
| [41] | Opgen-Rhein, R. and Strimmer, K. (2007). From correlation to causation networks: A simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst. Biol. 1 37. · Zbl 1166.62361 |
| [42] | Pesaran, M. H. and Yamagata, T. (2017). Testing for alpha in linear factor pricing models with a large number of securities. USC-INET Research Paper No. 17-13, USC Dornsife Institute for New Economic Thinking. |
| [43] | Ramirez, R. N., El-Ali, N. C., Mager, M. A., Wyman, D., Conesa, A. and Mortazavi, A. (2017). Dynamic gene regulatory networks of human myeloid differentiation. Cell Systems 4 416-429. |
| [44] | Romano, J. P. and Wolf, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. J. Amer. Statist. Assoc. 100 94-108. · Zbl 1117.62416 · doi:10.1198/016214504000000539 |
| [45] | Tetlock, P. C. (2007). Giving content to investor sentiment: The role of media in the stock market. J. Finance 62 1139-1168. |
| [46] | van de Geer, S., Bühlmann, P., Ritov, Y. and Dezeure, R. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. Ann. Statist. 42 1166-1202. · Zbl 1305.62259 · doi:10.1214/14-AOS1221 |
| [47] | van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer, New York. · Zbl 0862.60002 · doi:10.1007/978-1-4757-2545-2 |
| [48] | Wu, W.-B. and Wu, Y. N. (2016). Performance bounds for parameter estimates of high-dimensional linear models with correlated errors. Electron. J. Stat. 10 352-379. · Zbl 1333.62172 · doi:10.1214/16-EJS1108 |
| [49] | Yuan, M. and Lin, Y. (2007). Model selection and estimation in the Gaussian graphical model. Biometrika 94 19-35. · Zbl 1142.62408 · doi:10.1093/biomet/asm018 |
| [50] | Zhang, X. and Cheng, G. (2017). Simultaneous inference for high-dimensional linear models. J. Amer. Statist. Assoc. 112 757-768. · doi:10.1080/01621459.2016.1166114 |
| [51] | Zhang, D. and Wu, W. B. (2017a). Gaussian approximation for high dimensional time series. Ann. Statist. 45 1895-1919. · Zbl 1381.62254 · doi:10.1214/16-AOS1512 |
| [52] | Zhang, D. and Wu, W. B. (2017b). Supplement material for “Gaussian approximation for high dimensional time series. Available at Ann. Statist. online. · doi:10.1214/16-AOS1512SUPP |
| [53] | Zhang, C.-H. and Zhang, S. S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 217-242. · Zbl 1411.62196 · doi:10.1111/rssb.12026 |
| [54] | Zhang, J. L., Härdle, W. K., Chen, C. Y. and Bommes, E. (2016). Distillation of news flow into analysis of stock reactions. J. Bus. Econom. Statist. 34 547-563. · doi:10.1080/07350015.2015.1110525 |
| [55] | Zhu, Y. and Bradic, J. (2018). Linear hypothesis testing in dense high-dimensional linear models. J. Amer. Statist. Assoc. 113 1583-1600. · Zbl 1409.62139 · doi:10.1080/01621459.2017.1356319 |
| [56] | Zhu, X., Pan, R., Li, G., Liu, Y. and Wang, H. (2017). Network vector autoregression. Ann. Statist. 45 1096-1123. · Zbl 1381.62256 · doi:10.1214/16-AOS1476 |
| [57] | Zhu, X., Wang, W., Wang, H. and Härdle, W. K. (2019). Network quantile autoregression. J. Econometrics 212 345-358 · Zbl 1452.62688 · doi:10.1016/j.jeconom.2019.04.034 |
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