Bootstrap inference for network vector autoregression in large-scale social network
Tóm tắt
A large amount of online social network data such as Facebook or Twitter are extensively generated by the growth of social network platforms in recent years. Development of a network time series model and its statistical inference are as important as the rapid progress on the social network technology and evolution. In this work we consider a network vector autoregression for the large-scale social network, proposed by Zhu et al. (Ann Stat 45(3):1096–1123, 2017), and study its bootstrap estimation and bootstrap forecast. In order to suggest a bootstrap version of parameter estimates in the underlying model, two bootstrap methods are combined together: stationary bootstrap and classical residual bootstrap. Consistency of the bootstrap estimator is established and the bootstrap confidence intervals are constructed. Moreover, we obtain bootstrap prediction intervals for multi-step ahead future values. A Monte-Carlo study illustrates better finite-sample performances of our bootstrap technique than those by the standard method.
Tài liệu tham khảo
Can, U., & Alatas, B. (2019). A new direction in social network analysis: Online social network analysis problems and applications. Physica A: Statistical Mechanics and Its Applications, 535, 122372.
Chernozhukov, V., Härdle, W. K., Huang, C., & Wang, W. (2020). LASSO-driven inference in time and space. Annals of Statistics. arxiv:1806.05081v4(forthcoming).
Clements, M. P., & Taylor, N. (2001). Bootstrapping prediction intervals for autoregressive models. International Journal of Forecasting, 17, 247–267.
Durante, D., & Dunson, D. B. (2014). Nonparametric Bayes dynamic modelling of relational data. Biometrika, 101(4), 883–898.
Hwang, E., & Shin, D. W. (2012). Strong consistency of the stationary bootstrap under \(\psi\)-weak dependence. Statistics and Probability Letters, 82(3), 488–495.
Hwang, E., & Shin, D. W. (2013a). New bootstrap method for autoregressive models. Communications for Statistical Applications and Methods, 20(1), 85–96.
Hwang, E., & Shin, D. W. (2013b). Stationary bootstrap prediction intervals for GARCH(\(p, q\)). Communications for Statistical Applications and Methods, 20(1), 41–52.
Krampe, J., Kreiss, J. K., & Paparoditis, E. (2020). Bootstrap based inference for sparse high-dimensional time series models. Bernoulli. arXiv:1806.11083v3(forthcoming).
Nowicki, K., & Snijders, T. A. B. (2001). Estimation and prediction for stochastic block structures. Journal of American Statistical Association, 96, 1077–1087.
Pascual, L., Romo, J., & Ruiz, E. (2006). Bootstrap prediction for returns and volatilities in GARCH models. Computational Statistics and Data Analysis, 50, 2293–2312.
Patton, A., Politis, D. N., & White, H. (2009). Correction to “Automatic block-length selection for the dependent bootstrap” by D. Politis and H. White. Econometric Reviews, 28, 372–375.
Politis, D. N., & Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association, 89, 1303–1313.
Politis, D. N., & White, H. (2004). Automatic block-length selection for the dependent bootstrap. Econometric Reviews, 23, 53–70.
Staszewska-Bystrova, A. (2011). Bootstrap prediction bands for forecast paths from vector autoregressive models. Journal of Forecasting, 30, 721–735.
Thombs, L. A., & Schucany, W. R. (1990). Bootstrap prediction intervals for autoregression. Journal of American Statistical Association, 85, 486–492.
Wang, Y. J., & Wong, G. Y. (1987). Stochastic blockmodels for directed graphs. Journal of American Statistical Association, 82, 8–19.
Wei, F., & Tian, W. (2018). Heterogeneous connection effects. Statistics and Probability Letters, 133, 9–14.
Wolf, M., & Wunderli, D. (2015). Bootstrap joint prediction regions. Journal of Time Series Analysis, 36, 352–376.
Zhao, Y., Levina, E., & Zhu, J. (2012). Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics, 40, 2266–2292.
Zhu, X., Pan, R., Liu, Y., & Wang, H. (2017). Network vector autoregression. Annals of Statistics, 45(3), 1096–1123.
Zhu, X., Wnag, W., Wang, H., & Härdle, W. K. (2019). Network quantile autoregression. Journal of Econometrics, 212, 345–358.
Zhu, X., Huang, D. Pan, & Wang, H. (2020). Multivariate spatial autoregressive model for large scale social networks. Journal of Econometrics, 215, 591–606.