Weighted L₁-estimates for a VAR(p) time series model

References

• Brockwell , P. J. and Davis , R. A. 2002 . Introduction to Time Series and Forecasting , 2 , New York : Springer-Verlag .
   Google Scholar
• Krengel , U. 1985 . Ergodic Theorems , Vol. 6 , Berlin : Walter de Gruyter & Co . de Gruyter Studies in Mathematics
   Google Scholar
• Terpstra , J. T. and Rao , M. B. 2002 . On the asymptotic distribution of a multivariate GR-estimate for a VAR(p) time series . Statist. Probab. Lett , 60 : 219 – 230 .
   Google Scholar
• Lütkepohl , H. 1993 . Introduction to Multiple Time Series Analysis , 2 , Berlin : Springer-Verlag .
   Google Scholar
• Fuller , W. A. 1996 . Introduction to Statistical Time Series , 2 , New York : John Wiley & Sons, Inc .
   Google Scholar
• Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection , New York : Wiley .
   Google Scholar
• Heathcote , C. R. and Welsh , A. H. 1988 . Multivariate functional least squares . J. Multivariate Anal , 25 : 45 – 64 .
   Google Scholar
• Bustos , O. H. and Yohai , V. J. 1986 . Robust estimates for ARMA models . J. Amer. Statist. Assoc , 81 : 155 – 168 .
   Web of Science ®Google Scholar
• Li , W. K. and Hui , Y. V. 1989 . Robust multiple time series modelling . Biometrika , 76 : 309 – 315 .
   Google Scholar
• Ben , M. G. , Martinez , E. J. and Yohai , V. J. 1999 . Robust estimation in vector autoregressive moving-average models . J. Time Ser. Anal , 20 : 381 – 399 .
   Google Scholar
• Rao , C. R. 1988 . Methodology based on the L1-norm, in statistical inference . Sankhyā Ser. A , 50 : 289 – 313 .
   Google Scholar
• Koenker , R. and Portnoy , S. 1990 . M estimation of multivariate regressions . J. Amer. Statist. Assoc , 85 : 1060 – 1068 .
   Web of Science ®Google Scholar
• Davis , J. B. and McKean , J. W. 1993 . Rank-based methods for multivariate linear models . J. Amer. Statist. Assoc , 88 : 245 – 251 .
   Web of Science ®Google Scholar
• Bai , Z. D. 1990 . Asymptotic theory of least distances estimate in multivariate linear models . Statistics , 21 : 503 – 519 .
   Google Scholar
• Hettmansperger , T. P. and McKean , J. W. 1998 . Robust Nonparametric Statistical Methods , Vol. 5 , London : Edward Arnold . Kendall's Library of Statistics
   Google Scholar
• Gross , S. and Steiger , W. L. 1979 . Least absolute deviation estimates in autoregression with infinite variance . J. Appl. Probab , 16 : 104 – 116 .
   Google Scholar
• An , H. Z. and Chen , Z. G. 1982 . On convergence of LAD estimates in autoregression with infinite variance . J. Multivariate Anal , 12 : 335 – 345 .
   Web of Science ®Google Scholar
• Bloomfield , P. and Steiger , W. L. 1983 . Least Absolute Deviations , Vol. 6 , Boston, MA : Birkhäuser Boston Inc . Progress in Probability and Statistics
   Google Scholar
• Koul , H. L. and Ossiander , M. 1994 . Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression . Ann. Statist , 22 : 540 – 562 .
   Web of Science ®Google Scholar
• Koul , H. L. and Saleh , A. K.M.E. 1995 . Autoregression quantiles and related rank-scores processes . Ann. Statist , 23 : 670 – 689 .
   Web of Science ®Google Scholar
• Denby , L. and Martin , R. D. 1979 . Robust estimation of the first-order autoregressive parameter . J. Amer. Statist. Assoc , 74 : 140 – 146 .
   Web of Science ®Google Scholar
• Bustos , O. H. 1982 . General M-estimates for contaminated pth-order autoregressive processes: consistency and asymptotic normality. Robustness in autoregressive processes . Z. Wahrsch. Verw. Gebiete , 59 : 491 – 504 .
   Web of Science ®Google Scholar
• Künsch , H. 1984 . Infinitesimal robustness for autoregressive processes . Ann. Statist , 12 : 843 – 863 .
   Web of Science ®Google Scholar
• Martin , R. D. and Yohai , V. J. 1991 . “ Bias robust estimation of autoregression parameters ” . In Directions in Robust Statistics and Diagnostics, Part I, Vol. 33 of IMA Vol. Math. Appl , 233 – 246 . New York : Springer .
   Google Scholar
• Boldin , M. V. 1994 . On median estimates and tests in autoregressive models . Math. Methods Statist , 3 : 114 – 129 .
   Google Scholar
• Terpstra , J. T. 2002 . Letter to the editor: the existence of the first negative moment revisited . Amer. Statist , 56 : 254
   Google Scholar
• Hall , P. and Heyde , C. C. 1980 . Martingale Limit Theory and its Application , New York : Academic Press, Inc .
   Google Scholar
• Bose , A. and Chaudhuri , P. 1993 . On the dispersion of multivariate median . Ann. Inst. Statist. Math , 45 : 541 – 550 .
   Web of Science ®Google Scholar
• Heiler , S. and Willers , R. 1988 . Asymptotic normality of R-estimates in the linear model . Statistics , 19 : 173 – 184 .
   Google Scholar
• Terpstra , J. T. and Rao , M. B. 2001 . Generalized rank estimates for an autoregressive time series: a U-statistic approach . Stat. Inference Stoch. Process , 4 : 155 – 179 .
   Google Scholar
• Yoshihara , K. 1976 . Limiting behavior of U-statistics for stationary, absolutely regular processes . Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , 35 : 237 – 252 .
   Web of Science ®Google Scholar
• Bartle , R. G. 1976 . The Elements of Real Analysis , 2 , New York, London, Sydney : John Wiley & Sons .
   Google Scholar
• Jaeckel , L. A. 1972 . Estimating regression coefficients by minimizing the dispersion of the residuals . Ann. Math. Statist , 43 : 1449 – 1458 .
   Google Scholar
• Nocedal , J. and Wright , S. J. 1999 . Numerical Optimization , New York : Springer-Verlag .
   Google Scholar
• Naranjo , J. D. and Hettmansperger , T. P. 1994 . Bounded influence rank regression . J. R. Stat. Soc. Ser. B , 56 : 209 – 220 .
   Google Scholar
• Fox , A. J. 1972 . Outliers in time series . J. R. Stat. Soc. B , 34 : 350 – 363 .
   Google Scholar
• Terpstra , J. T. , McKean , J. W. and Naranjo , J. D. 2001 . Weighted Wilcoxon estimates for autoregression . Aust. N. Z. J. Stat , 43 : 399 – 419 .
   Web of Science ®Google Scholar
• Ooms , M. 1994 . Empirical Vector Autoregressive Modeling , Vol. 407 , Berlin : Springer-Verlag . Lecture Notes in Economics and Mathematical Systems
   Google Scholar