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Robust time series analysis: a survey. (English) Zbl 0652.62088
Kybernetika 23, Suppl. No. 1-5, 92 pp. (1987).
The paper is divided into 5 chapters. The first chapter introduces general concepts of robustness and standard time series models. The second chapter is devoted to maximum likelihood type estimation (MLTE) in AR and ARMA models. Robust estimation of the location of ARMA models is also included.
Generalized MLTE is described in the third chapter. Some sub-sections are devoted to determining outlier type and to model selection problems. The next chapter deals with robust filtering and robust smoothing. The last chapter contains some Monte Carlo results and topics for further research.
The authors explain basic ideas and important properties of the described procedures. The proofs of assertions are not given in the paper, but the reader is systematically informed where they can be found.
The paper is a readable review of robust methods in time series analysis and brings clear description of algorithms of the corresponding numerical procedures.
Reviewer: J.Anděl

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F35 Robustness and adaptive procedures (parametric inference)
Software:
COVINTER; ROBETH; BLINWDR
Full Text: EuDML
References:
[1] Abraham B., G. E. P. Box (1979): Bayesian Analysis of Some Outlier Problems in Time Series. Biometrika 66, 229-236. · Zbl 0407.62063
[2] Ahrens J. H., U. Dieter (1974): Computer Methods for Sampling from Gamma, Beta, Poisson and Binomial Distributions. Computing 12, 223 - 246. · Zbl 0285.65009
[3] Akaike H. (1969): Power Spectrum Estimation through Autoregressive Model Fitting. Ann. Inst. Statist. Math. 21, 407-419. · Zbl 0218.62113
[4] Akaike H. (1974): A New Look at the Statistical Model Identification. IEEE Trans. Automat. Control. AC-19, 716-722. · Zbl 0314.62039
[5] Anderson T. W. (1971): The Statistical Analysis of Time Series. John Wiley, New York. · Zbl 0225.62108
[6] Andrews D. F. P. J. Bickel F. R. Hampel P. J. Huber W. H. Rogers, J. W. Tukey (1972): Robust Estimates of Location; Survey and Advances. Princeton University Press, Princeton. · Zbl 0254.62001
[7] Beaton A. E., J. W. Tukey (1974): The Fitting of Power Series, Meaning Polynomials, Illustrated on Bandspectroscopic Data. Technometrics 16, 2, 147-197. · Zbl 0282.62057
[8] Boente G. R. Fraiman, V. J. Yohai (1982): Qualitative Robustness for General Stochastic Processes. Techn. Rep. 26, Dept. Statist., Univ. Washington, Seattle. · Zbl 0644.62037
[9] Box G. E. P., G. M. Jenkins (1976): Time Series Analysis: Forecasting and Control. HoldenDay, San Francisco. · Zbl 0363.62069
[10] Box. G. E. P., G. C. Tiao (1975): Intervention Analysis with Applications to Economic and Environmental Problems. J. Amer. Statist. Assoc. 70, 70-79. · Zbl 0316.62045
[11] Brubacher S. R. (1974): /: Time Series Outlier Detection and Modeling with Interpolation. Bell Laboratories Techn. Mem.
[12] Bustos O. H. (1981): Qualitative Robustness for General Processes. Informes de Matematica, Serie B-002/81, Institute de Matematica Pura e Aplicada, Rio de Janeiro.
[13] Bustos O. H. (1982): General M-Estimatcs for Contaminated \(pth\)-Order Autoregressive Processes: Consistency and Asymptotic Normality. Z. Wahrsch. verw. Gebiete 59, 491 - 504. · Zbl 0482.62080
[14] Bustos O R. Fraiman, V. J. Yohai (1984): Asymptotic Behavior of Estimates Based on Residual Autocovariances for ARMA Models. Informes de Matematica, Serie B-019-Junho/84, Instituto de Matematica Pura e Aplicada, Rio de Janeiro. To appear in Proc. Heidelberg Workshop on Robust and Nonlinear Time Series, Sept. 1983. · Zbl 0565.62067
[15] Bustos O. H., V. J. Yohai (1983): Robust Estimates for ARMA Models. Manuscript. Submitted to J. Amcr. Statist. Soc.
[16] Chernick M. R. D. J. Downing, D. H. Pike (1982): Detecting Outliers in Time Series Data. J. Amer. Statist. Assoc. 77, 380.
[17] Cleveland W. S. (1979): Robust Locally Weighted Regression and Smoothing Scatterplots. J. Amer. Statist. Assoc. 74, 368, 829-836. · Zbl 0423.62029
[18] Cleveland W. S. (1982): A Reader’s Guide to Smoothing Scatterplots and Graphical Methods for Regression. Modern Data Analysis (Launer and Siegel Acad. Press, New York.
[19] Cox D. D. (1981): Metrics on Stochastic Processes and Qualitative Robustness. Techn. Rep. 3, Dept. Statist., Univ. Washington, Seattle.
[20] Denby L., W. Larsen (1977): Robust Regression Estimators Compared via Monte Carlo. Commun. Statist. A 6, 4, 335-362. · Zbl 0379.62059
[21] Denby L., R. D. Martin (1979): Robust Estimation of the First-Order Autoregressive Parameter. J. Amer. Statist. Assoc. 74, 365, 140-146. · Zbl 0407.62066
[22] Devlin S. J. R. Gnanadesikan, J.R. Kettenring 1975): Robust Estimation and Outlier Detection with Correlation Coefficients. Biometrika 62, 531 - 545. · Zbl 0321.62053
[23] Donoho D. L., P. J. Huber (1983): The Notion of Breakdown Point. Festschrift for Erich L. Lehmann (Bickel et al.. Wadsworth, Belmont, CA. · Zbl 0523.62032
[24] Durbin J. (1959): Efficient Estimation of Parameters in Moving Average Models. Biometrika 46, 306-316. · Zbl 0097.34602
[25] Dutter R. (1975): Robust Regression: Different Approaches to Numerical Solutions and Algorithms. Res. Rep. 6, Fachgruppe f. Statist., Eidgen. Techn. Hochsch., Zürich.
[26] Dutter R. (1980): Robuste Regression. Bericht 135, Math. Statist. Sektion im Forschungszentrum Graz. · Zbl 0442.62035
[27] Dutter R. (1983): COVINTER: A Computer Program for Computing Robust Covariances and for Plotting Confidence Ellipses. Res. Rep. 10, Inst. for Statist., Techn. Univ. Graz.
[28] Dutter R. (1983b): Computer Program BLINWDR for Robust and Bounded Influcnce Regression Res. Rep. 8, Inst. Statist., Techn. Univ. Graz.
[29] Duttcr R., P. J. Huber (1981): Numerical Mcthods for the Nonlinear Robust Regression Problem. J. Statist. Comput. Simul. 13, 2, 79-114.
[30] Fox A. J. (1972): Outliers in Time Series. J. Roy. Statist. Soc. B, 34, 3, 350-363. · Zbl 0249.62089
[31] Fuller W. A. (1976): Introduction to Statistical Time Series. John Wiley, New York. · Zbl 0353.62050
[32] Gastwirth J. L., H. Rubin (1975): The Behavior of Robust Estimators on Dependent Data. Ann. Statist 3, 5, 1070-1100. · Zbl 0359.62042
[33] Grenander V., Mi Rosenblatt (1957): Statistical Analysis of Stationary Time Series. John Wiley, New York. · Zbl 0080.12904
[34] Hampel F. R. (1968): Contributions to the Theory of Robust Estimation. Ph. D. Thesis. University of California, Berkeley.
[35] Hampel F. R. (1971): A General Qualitative Definiticn of Robustness. Ann. Math. Statist. 42, 6, 1887-1896. · Zbl 0229.62041
[36] Hampel F. R. (1973): Robust Estimation: A Condensed Partial Survey. Z. Wahrsch. verw. Gebiete 27, 87-104. · Zbl 0255.62045
[37] Hampel F. R. (1974): The Influence Curve and Its Role in Robust Estimation. J. Amer. Statist. Assoc. 69 346, 383-393. · Zbl 0305.62031
[38] Hampel F. R. (1975): Beyond Location Parameters: Robust Concepts and Methods. ISI Invited Paper, Proceedings of the 40th Session, Vol. XLVI, Book I, 375 - 382. Warsaw.
[39] Hampel F. R.. A. Marazzi. E. Ronchetti P. Rousseeuw W. Stahcl, R. E. Welsch. (1982): Robust Statistical Methods, Handouts for the Instructional Meeting on. Part IV. Palermo, Italy, Sept. 10-11, 1982.
[40] Hampel F. R. W. A. Stahel E. M. Ronchetti, P. J. Rousseeuw (1986): Robust Statistics: The Approach Based on Influence Functions. John Wiley, New York. · Zbl 0593.62027
[41] Hannan E. J. (1970): Multiple Time Series. John Wiley, New York. · Zbl 0211.49804
[42] Hannan E. J. (1973): The Asymptotic Theory of Linear Time Series Models. J. Appl. Prob. 10, 130-145. · Zbl 0261.62073
[43] Hannan E. H., M. Kanter (1977): Autoregressive Processes with Infinite Variance. J. Appl. Prob. 14, 411-415. · Zbl 0366.60033
[44] Huang T. S. G. J. Yang, G. Y. Tang (1979): A Fast Two-Dimensional Median Filtering Algorithm. IEEE Trans. Acoust. Speech Signal Process. 27, 1, 13-18.
[45] Huber P. J. (1964): Robust Estimation of a Location Parameter. Ann. Math. Statist. 35, 1, 73-101. · Zbl 0136.39805
[46] Huber P. J. (1973): Robust Regression: Asymptotics, Conjectures and Monte Carlo. Ann. Statist. 1, 5, 799-821. · Zbl 0289.62033
[47] Huber P. J. (1977): Robust Covariances. Statistical Decision Theory and Related Topics (Gupta S. and D. Moore, Vol. II. Academic Press, New York. · Zbl 0435.62041
[48] Huber P. J. (1979): Robust Smoothing. Robustness in Statistics (Launer and Wilkinson. Academic Press, New York.
[49] Huber P. J. (1981): Robust Statistics. John Wiley, New York. · Zbl 0536.62025
[50] Huber P. J. (1982): Current Issues in Robust Statistics. Some Recent Advances in Statistics (Tiago de Oliveira and Epstein Acad. Press, New York. · Zbl 0555.62034
[51] Jazwinski A. (1970): Stochastic Processes and Filtering Theory. Acad. Prcss, New York. · Zbl 0203.50101
[52] Jones R. H. (1980): Maximum Likelihood Fitting of ARMA Models to Time Series with Missing. Observations. Technometrics 22, 3. · Zbl 0451.62069
[53] Justusson B. (1977): Statistical Properties of Median Filters in Signal and Image Processing. Unpubl. Rcp., Math. lnstitut., Royal Instit. of Techn., Stockholm. Svveden.
[54] Kailath T. (1968): An Innovations Approach to Linear Least Squares Estimation and Filtering. IEEE Trans. Automat. Control. AC-13, 6, 646 - 655.
[55] Kanter M., W. L. Steiger (1974): Regression and Autoregression With Infinite Variance. Adv. in Appl. Prob. 6, 768-783. · Zbl 0317.62043
[56] Kassam S. A., H. V. Poor (1985): Robust Techniques for Signal Processing: A Survey. Proc. IEEE 73, 3. · Zbl 0569.62084
[57] Kleiner R. R. D. Martin, D. J. Thomson (1979). : Robust Estimation of Powcr Spectra. J. Royal Statist. Soc. B 41, 3, 313-338. · Zbl 0421.62069
[58] Krasker W. S., R. E. Welsch (1982): Efficient Bounded-Infiuence Regression Estimation. J. Amer. Statist. Soc. 77, 379, 595-604. · Zbl 0501.62062
[59] Kuensch H. (1983a): Infinitesimal Robustness for AutoregressiveProcesses. Res. Rep. 38, Fachgr. Statistik, ETH Zürich.
[60] Kuensch H. (1983b): The Influence Function and Optimal Robust Estimators for Time Serics. Subm. to Ann. Statist.
[61] Lee C. H. (1981): M-Estimates for ARMA Processes. Ph. D. Thesis. Dept. Elect. Engin., Univ. Washington. Seattle.
[62] Lee C. H., R. D. Martin (1982): M-Estimates for ARMA Processes. Techn. Rep. 23, Dept. Statist. Univ. Washington, Seattle.
[63] Lee C. H., R. D. Martin (1982b): The Information Matrix and Robust M-Estimates for ARMA Processes. Techn. Rep. 24, Dept Statist, Univ. Washington, Seatle.
[64] Lee C. H., R. D. Martin (1984): Ordinary and Proper Location M-Estimates for ARMA Models. Techn. Rep. 29, Dept. Statist., Univ. Washington, Seattle.
[65] Lenth R. V. (1977): Robust Splines. Commun. Stalist A 6, 847-854. · Zbl 0368.62047
[66] Mallows C. L. (1976): On Some Topies in Robustness. Bell Laboratories, Techn, Memo., Murray Hill, New Jersey.
[67] Mallows C. L. (1980a): Resistant Smoothing. Time Series (Anderson O. D.. North-Holland Publishing Company. · Zbl 0447.62092
[68] Mallows C. L. (1980b): Some Theory of Nonlinear Smoothers. Ann. Statist 8, 4, 695-715. · Zbl 0446.62100
[69] Mann H. B., A. Wald (1943): On the Statistical Treatment of Linear Stochastic Differcnce Equations. Econometrica 11, 173 - 220. · Zbl 0063.03773
[70] Marazzi A. (1980): Robust Affine Invariant Covariances in ROBETH. Res. Rep. 24, Eidgenössische Techn. Hochschule, Zürich.
[71] Maronna R. (1976): Robust M-Estimation of Multivariate Location and Scatter. Ann. Statist 4 1, 51-67. · Zbl 0322.62054
[72] Maronna R. O. Bustos, V. J. Yohai (1979): Bias- and Efficiency-Robustness of General M-Estimators for Regression with Random Carriers. Smoothing Techniques for Curve Estimation - Proc. Heidelberg (Gasser Th. and M. Rosenblatt. Lecture Notes in Math. 757, Springer, Berlin. · Zbl 0416.62050
[73] Martin R. D. (1978a): Asymptotic Properties of M-estimates for pth-order Autoregressions. Techn. Rep. 212, Dept. Electrical Engineering, Univ. Washington, Seattle.
[74] Martin R. D. (1978b): Robust Estimates of the Mean with Autoregressive Errors. Techn. Rep. 211, Dept Electrical Engineering, Univ. Washington, Seattle.
[75] Martin R. D. (1978c): Asymptotic Properties of Generalized M-estimates for Autoregressive Parameters. Techn. Rep. 213, Dept. Elec. Engng., Univ. Washington, Seattle.
[76] Martin R. D. (1979): Robust Estimation for Time Series Autoregressions. Robustness in Statistics (Launer and Wilkinson Acad. Press, New York.
[77] Martin R. D. (1979b): Robust Estimation of Location with Autoregressive Errors. Unpubl. manuscript, Dept. Electrical Engineering, Univ. Washington, Seattle.
[78] Martin R. D. (1979c): Approximate Conditional-Mean Type Smoothers and Interpolators. Smoothing Techniques for Curve Estimation - Proc. Heidelberg, 1979. (Gasser and Rosenblatt. Springer-Verlag. New York. · Zbl 0423.62073
[79] Martin R. D. (1980): Robust Estimation of Autoregressive Models. Directions in Time Series. (Brillinger D. R. and G. C. Tiao. Inst. Math. Statist. Publications, Haywood, CA, pp. 228-254.
[80] Martin R. D. (1980b): Time Series: Model Estimation, Data Analysis and Robust Procedures. Proc. Symp. Appl. Math., (R. V. Hogg, Vol. 23. · Zbl 0441.62079
[81] Martin R. D. (1981): The Cramer-Rao Bound and Robust M-Estimates for Autoregressions. Techn. Rep. 9, Dept. Statist., Univ. Washington, Seattle. · Zbl 0499.62029
[82] Martin R. D. (1981b): Robust Methods for Time Series. Applied Time Series II (Findley. Acad. Press, New York.
[83] Martin R. D. (1982): The Cramer-Rao Bound and Robust M-Estimates for Autoregressions. Biometrika 69, 2, 437-442. · Zbl 0499.62029
[84] Martin R. D. (1983): Robust-Resistant Spectral Analysis. Handbook of Statistics. Vol. 3 (Brillinger and Krishnaiah. Elsevier Sc. Publ. B. V.
[85] Martin R. D. (1984): Robust-Resistant Spectral Analysis. Techn. Rep. 27, Dept. Statist., Univ. Washington, Seattle. · Zbl 0536.62076
[86] Martin R. D., G. De Bow (1976): Robust Filtering with Data-Dependent Covariance. Proc. John Hopkins Conference and Informations Sciences and Systems, March 31 - April 2.
[87] Martin R. D., J. M. Jong (1976): Asymptotic Properties of Robust Generalized M-Estimales for the First-Order Autoregressive Parameter. Bell Laboratories Techn. Memo., Murray Hill, New Jersey.
[88] Martin R. D., C. H. Lee (1980): Robust Estimation of Location with Autoregressive Errors. Manuscript. Dept. Statist., Univ. Washington, Seattle.
[89] Martin R. D. A. Samarov, W. Vandaele (1983): Robust Methods for ARIMA Models. Applied Time Series Analysis of Economic Data (Zellner. Econ. Res. Rep. ER-5, Bureau of the Census. Washington, DC.
[90] Martin R. D., D. J. Thomson (1982): Robust-Resistant Spectrum Estimation. Proc. IEEE 70, 9.
[91] Martin R. D., V. J. Yohai (1984a): Robustness in Time Series and Estimating ARMA Models. Techn. Rep. 50, Dept. Statist., Univ. Washington. Seattle.
[92] Martin R. D., V. J. Yohai (1948b): Influence Curves for Time Series. Techn. Rep. 51, Dept. Statist., Univ. Washington. Seattle.
[93] Martin R. D., J. E. Zeh (1977): Determining the Character of Time Series Outliers. Proc. Amer. Statist. Assoc, Business and Economics Section.
[94] Martin R. D., J. E. Zeh (1979): Generalized M-estimates for Autoregressions, Including Small-Sample Efficiency Robustness. Techn. Rep. 214, Department of Electrical Engineering, University of Washington, Seattle.
[95] Masreliez C. J. (1975): Approximate Non-Gaussian Filtering with Linear State and Observation Relations. IEEE Trans. Automat. Control AC-20, 107-110. · Zbl 0298.93018
[96] Masreliez C. J., R. D. Martin (1977): Robust Bayesian Estimation for the Linear Model and Robustifying the Kalman Filter. IEEE Trans. Automat. Control AC-22, 361 - 371. · Zbl 0354.93054
[97] Mosteller F., J. W. Tukey (1977): Data Analysis and Regression. Addison-Wesley, Reading, MA.
[98] Nagel G., W. Wolff (1974): Ein Verfahren zur Minimierung einer Quadratsumme nichtlinearer Funktionen. Biometrische Zeitschr. 16, 6, 431 - 439. · Zbl 0294.65037
[99] Pagano M. (1974): Estimation of Models of Autoregressive Signal Plus White Noise. Ann. Statist. 2, 99-108. · Zbl 0317.62059
[100] Papantoni-Kazakos P., R. M. Gray (1979): Robustness of Estimators of Stationary Observations. Ann. Probab. 7, 6, 989- 1002. · Zbl 0426.62021
[101] Parzen E. (1971): Efficient Estimation of Stationary Time Series Mixed Schemes. Proc. 39th Session of ISI, Washington, D. C. · Zbl 0231.62102
[102] Parzen E. (1974): Some Recent Advances in Time Series Modelling. IEEE Trans. Automat. Control AC-19, 723-730. · Zbl 0317.62063
[103] Polasek W. (1982): Robust Estimation and Resistance Analysis for the Autocorrelation Function. Preprint 47, Univ. Vienna.
[104] Polasek W. (1982b). : Exploratory Business-cycle Analysis Using Running Medians. Empirica 1, 49-70.
[105] Polasek W., R. Mertl (1983): Robust and Jackknife Estimators of the Autocorrelation Function. Res. Rep., Inst. Statist, and Informatics, Univ. Vienna.
[106] Rabiner L. R. M. R. Sambur, C. E. Schmidt (1975): Applications of a Nonlinear Smoothing Algorithm to Speech Processing. IEEE Trans. Acoust. Speech Signal Process ASSP-23, 552-557.
[107] Reinisch C. H. (1967): Smoothing by Spline Functions. Numer, Mathem. 10, 177-183, and Numer. Mathem. 16, 451-454. · Zbl 0161.36203
[108] Relies D. A. (1968): Robust Regression by Modified Least Squares. Ph. D. Thesis. Dept. Statist., Yale University.
[109] Rieder H. (1980): Locally Robust Correlation Coefficients. Commun. Statist. A9, 8, 803 - 819. · Zbl 0436.62036
[110] Schweppe F. (with E. Handschin J. Kohlas, A. Friechter) (1975): Bad Data Analysis for Power System State Estimation. IEEE Trans. Power Apparatus Systems 94, 2, 329-337.
[111] Serfling R. J. (1980): Approximation Theorems of Mathematical Statistics. John Wiley, New York. · Zbl 0538.62002
[112] Shibata R. (1976): Selection of the Order of an Autoregressive Model by Akaike’s Information Criterion. Biometrika 63, 1, 117-128. · Zbl 0358.62048
[113] Siddiqui M. M. (1958): On the Inversion of the Sample Covariance Matrix in a Stationary Autoregressive Process. Ann. Math. Statist. 29, 585-588. · Zbl 0099.14305
[114] Stadlober E., U. Dieter (1985): Computer Methods for Generating Student \(t\)-Variatcs. To appear in Computing.
[115] Stockinger N. (1983): Robust Estimation of Autoregressive Moving Average Models. Proc. of the 4th Pannonian Symposium on Math. Statist., Bad Tatzmannsdorf, Austria (Grossmann, Konecny, Pflug, Vincze and Wertz, pp. 299-309. Reidel Publ. Comp., Dordrecht-Holland.
[116] Stockinger N. (1984): Detection of Outliers in Arrhythmic Pressure Pulses by Robust Methods of Time Series Analysis. Res. Rep. 11, Inst. Statist., Tcchn. Univ. Graz.
[117] Stockinger N. (1985a): Generalized Maximum Likelihood Type Estimation of Autoregressive Moving Average Models. Ph. D. Thesis, Techn. Univ. Graz.
[118] Stockinger N. (1985b): Computer Programs for the Simulation and GM-Estimation of ARMA models. Res. Rep. TS-1985-2; Inst. Statist, and Wahrscheinlichkeitstheorie, Techn. Univ. Vienna.
[119] Stockinger N., R. Dutter (1983): Robust Time Series Analysis - An Overview. Res. Rep. 9, Inst. Statist., Techn. Univ. Graz. · Zbl 0652.62088
[120] Stockinger N. K. P. Pfeiffer, R. Dutter (1984): Ausreissererkennung in Arrhythmischen Druckpulsen durch Robuste Methoden der Zeitreihenanalyse. Medizinische Informatik ’84 (Gell and Eichtinger, Schriftenreihe der Oesterr. Computer Ges., Vol. 24, Oldenbourg Verlag, Vienna.
[121] Stuetzle W. (1979): Asymptotics for Running M-Estimates. Smoothing Techniques for Curve Estimation- Proc. Heidelberg, 1979 (Gasser and Rosenblatt. Springer-Verlag, New York.
[122] Thomson D. J. (1977): Spectrum Estimation Techniques for Characterization and Development of WT 4 Waveguide - I. Bell System Techn. J. 56, 4, 1769- 1815.
[123] Tukey J. W. (1960): A Survey of Sampling from Contaminated Distributions. Contributions to Probability and Statistics (I. Olkin. Stanford University Press, Stanford, CA. · Zbl 0201.52803
[124] Tukey J. W. (1977): Explorative Data Analysis. Addison Wesley, Reading, MA.
[125] Tukey J. W., T. E. Harris (1949): Development of Large-Sample. Measures of Location and Scale Which Are Relatively Insensitive to Contamination (Sampling from Contaminated Distributions, 3). Memorandum Rep. 31, Statist. Research Group, Princeton University, New Jersey.
[126] Velleman P. F. (1975): Robust Nonlinear Data Smoothers; Theory, Definitions and Applications. Ph. D. Thesis, Dept. Statist., Princeton University.
[127] Velleman P. F. (1980): Definition and Comparison of Robust Nonlinear Data Smoothing Algorithms. J. Amer. Statist. Assoc. 75, 371, 609-615. · Zbl 0455.62002
[128] Walker A. M. (1960): Some Consequences of Superimposed Error in Time Series Analysis. Biometrika 47, 33-43. · Zbl 0099.13702
[129] Wegman E. J., R. J. Carrol (1977): A Monte Carlo Study of Robust Estimators of Location. Comimin. Statist. - Theor. Meth. A 6, 9, 795-812. · Zbl 0372.62017
[130] Whittle P. (1952): Estimation and Information in Stationary Time Series. Arkiv foer Matematik 2, 23, 423-434. · Zbl 0053.41003
[131] Wilson G. T. (1969): Factorization of the Generating Function of a Pure Moving Average Process. SIAM J. Num. Analysis 6, 1. · Zbl 0176.46401
[132] Yohai V. J, and R. A. Maronna (1977): Asymptotic Behavior of Least Squares Estimates for Autoregressive Processes with Infinite Variances. Ann. Statist. 5, 3, 554-560. · Zbl 0378.62075
[133] Zeh J. E. (1979): Efficiency Robustness of Generalized M-Estimates for Autoregrcssion and Their Use in Determining Outlier Type. Ph. D. Thesis, Univ. Washington, Seattle.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.