Simultaneous sparse model selection and coefficient estimation for heavy-tailed autoregressive processes

References

• Akaike H. Fitting autoregressive models for prediction. Ann Inst Stat Math. 1969;21:243–247. doi: 10.1007/BF02532251
   Web of Science ®Google Scholar
• Poskitt DS. Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases. Ann Inst Math Stat. 2007;59:697–725. doi: 10.1007/s10463-006-0074-4
   Web of Science ®Google Scholar
• Shibata R. Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Ann Stat. 1980;8:147–164. doi: 10.1214/aos/1176344897
   Web of Science ®Google Scholar
• Galbraith JW, Zinde-Walsh V. On Some simple autoregression-based estimation and identification techniques for ARMA models. Biometrika. 1997;84:685–696. doi: 10.1093/biomet/84.3.685
   Web of Science ®Google Scholar
• Galbraith JW, Zinde-Walsh V. Autoregression-based estimators for ARFIMA models. CIRANO Working Papers. 2001s-11.
   Google Scholar
• Ing C, Wei C. Order selection for same-realization predictions in autoregressive processes. Ann Stat. 2005;33:2423–2474. doi: 10.1214/009053605000000525
   Web of Science ®Google Scholar
• Akaike H. Maximum likelihood identification of Gaussian autoregressive moving average model. Biometrica. 1973;60:255–265. doi: 10.1093/biomet/60.2.255
   Web of Science ®Google Scholar
• Akaike H. Statistical predictor identification. Ann Inst Stat Math. 1970;22:203–217. doi: 10.1007/BF02506337
   Web of Science ®Google Scholar
• Schwarz GE. Estimating the dimension of a model. Ann Stat. 1978;6:461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• Stein CM. Estimation of the mean of a multivariate normal distribution. Ann Stat. 1981;9:1135–1151. doi: 10.1214/aos/1176345632
   Web of Science ®Google Scholar
• S. Ralescu, Brandwein AC, Strawderman WE. Stein estimation for non-normal spherically symmetric location families in three dimensions. J Multivariate Anal. 1992;42:35–50. doi: 10.1016/0047-259X(92)90077-S
   Web of Science ®Google Scholar
• Brandwein AC, Ralescu S, Strawderman WE. Shrinkage estimators of the location parameter for certain spherically symmetric distributions. Ann Inst Stat Math. 1993;45:551–565. doi: 10.1007/BF00773355
   Web of Science ®Google Scholar
• Tibshirani RJ. Regression shrinkage and selection via the LASSO. J R Stat Soc, B. 1996;58:267–288.
   Google Scholar
• Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc. Theory Methods. 2001;96:1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• Zou H. The adaptive LASSO and its oracle properties. J Am Stat Assoc. 2006;101:1418–1429. doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar
• Fan J, Li R. Variable selection for Cox's proportional hazards model and frailty model. Ann Stat. 2002;30:74–99. doi: 10.1214/aos/1015362185
   Web of Science ®Google Scholar
• Fan J, Li R. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J Am Stat Assoc. 2004;99:710–723. doi: 10.1198/016214504000001060
   Web of Science ®Google Scholar
• Hunter DR, Li R. Variable selection using MM algorithm. Ann Stat. 2005;33:1617–1642. doi: 10.1214/009053605000000200
   PubMed Web of Science ®Google Scholar
• Yuan M, Lin Y. On the nonnegative garrote estimator. J R Stat Soc, B. 2007;69:143–161. doi: 10.1111/j.1467-9868.2007.00581.x
   Google Scholar
• Wu Y, Liu Y. Variable selection in quantile regression. Statistica Sin. 2009;19:801–817.
   Web of Science ®Google Scholar
• H. Wang, G. Li, and Tsai CL. Regression coefficient and autoregressive order shrinkage and selection via the lasso. J R Stat Soc, B. 2007;69:63–78.
   Google Scholar
• Yoon YJ, Park C, Lee T. Penalized regression models with autoregressive error terms. J Stat Comput Simul, iFirst. 2012:1–17.
   Google Scholar
• Nardi Y, Rinaldo A. Autoregressive process modeling via the Lasso procedure. J Multivariate Anal. 2011;102:528–549. doi: 10.1016/j.jmva.2010.10.012
   Web of Science ®Google Scholar
• Feigin PD, Resnick SI. Pitfalls of fitting autoregressive models for heavy-tailed time series. Extremes. 1999;1:391–422. doi: 10.1023/A:1009946321478
   Google Scholar
• Wooldridge JM. Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press; 2002.
   Google Scholar
• Brockwell PJ, Davis RA. Time series: theory and methods. New York: Springer-Verlag, New York, Inc.; 1987.
   Google Scholar
• Bickel PJ, Levina E. Regularized estimation of large covariance matrices. Ann Stat. 2008;36:199–227. doi: 10.1214/009053607000000758
   Web of Science ®Google Scholar
• Xiao H, Wu WB. Covariance matrix estimation for stationary time series. Ann Stat. 2012;40(1):466–493. doi: 10.1214/11-AOS967
   Web of Science ®Google Scholar
• Robinson PM. Time series residuals with application to probability density estimation. J Time Ser Anal. 1987;8(3):329–344. doi: 10.1111/j.1467-9892.1987.tb00445.x
   Google Scholar
• Liebscher E. Estimating the density of the residuals in autoregressive models. Stat Inference Stoch Process. 1999;2(2):105–117. doi: 10.1023/A:1009924821271
   Google Scholar
• Müller UU, Schick A, Wefelmeyer W. Weighted residual-based density estimators for nonlinear autoregressive models. Statistica Sin. 2005;15(1):177–195.
   Web of Science ®Google Scholar
• Frank I, Friedman J. A statistical view of some chemometrics regression tools. Technometrics. 1993;35:109–148. doi: 10.1080/00401706.1993.10485033
   Web of Science ®Google Scholar
• Zou H, Li R. One-step sparse estimates in nonconcave penalized likelihood models. Ann Stat. 2008;36:1509–1533. doi: 10.1214/009053607000000802
   PubMed Web of Science ®Google Scholar
• Hafner CM, Preminger A. Asymptotic theory for a factor GARCH model. Econom Theory. 2009;25:336–363. doi: 10.1017/S0266466608090117
   Web of Science ®Google Scholar
• Dudley RM. Real analysis and probability. Cambridge, UK: Cambridge University Press; 2002.
   Google Scholar
• Brown BM. Martingale central limit theorems. Ann Math Stat. 1971;42:59–69. doi: 10.1214/aoms/1177693494
   Google Scholar
• Pfanzagl J. On the measurability and consistency of minimum contrast estimates. Metrika. 1969;14:249–272. doi: 10.1007/BF02613654
   Web of Science ®Google Scholar
• Brockwell PJ, Lindner A. Strictly stationary solutions of autoregressive moving average equations. Biometrika. 2010:1–8.
   Google Scholar
• Mokkadem A. Mixing properties of ARMA processes. Stoch Process Appl. 1988;29:309–315. doi: 10.1016/0304-4149(88)90045-2
   Web of Science ®Google Scholar
• Billingsley P. Probability and measure. New York: Wiley; 1995.
   Google Scholar