ROBUST METHODS FOR TIME SERIES

Outliers in time series can wreak havoc with conventional least-squares procedures, just as in the case of ordinary regression. This paper presents two time-series outlier models, points out their ordinary regression analogues and the corresponding outlier patterns, and presents robust alternatives to the least-squares method of fitting autoregressive-moving-average models. The main emphasis is on robust estimation in the presence of additive outliers. This results in the problem having an errors-in-variables aspect. While several methods of robust estimation for this problem are presented, the most attractive approach is an approximate non-Gaussian maximum-likelihood type method which involves the use of a robust non-linear filter/one-sided interpolator with data-dependent scaling. Robust smoothing/two-sided outlier interpolation, forecasting, model selection, and spectral analysis are briefly mentioned, as are the problems of estimating location and dealing with trends, seasonality, and missing data. Some examples of applying the methodology are given.

[1]  F. Hampel.  A General Qualitative Definition of Robustness , 1971 .

[2]  S. Portnoy.  Robust Estimation in Dependent Situations , 1977 .

[3]  Y. Bar-Shalom.  Optimal simultaneous state estimation and parameter identification in linear discrete-time systems , 1972 .

[4]  L. Denby,et al.  Robust Estimation of the First-Order Autoregressive Parameter , 1979 .

[5]  E. Hannan.  The asymptotic theory of linear time-series models , 1973, Journal of Applied Probability.

[6]  M. Crowder.  Maximum Likelihood Estimation for Dependent Observations , 1976 .

[7]  M. Pagano.  Estimation of Models of Autoregressive Signal Plus White Noise , 1974 .

[8]  E. Tse,et al.  On the identifiability of parameters , 1971, CDC 1971.

[9]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise , 1968 .

[10]  D. Thomson.  Spectrum estimation techniques for characterization and development of WT4 waveguide–I , 1977, The Bell System Technical Journal.

[11]  C. Masreliez.  Approximate non-Gaussian filtering with linear state and observation relations , 1975 .

[12]  H. Akaike.  A new look at the statistical model identification , 1974 .

[13]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[14]  G. Tunnicliffe Wilson,et al.  Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand , 1976 .

[15]  Kenneth D. Garbade,et al.  Two Methods for Examining the Stability of Regression Coefficients , 1977 .

[16]  Richard H. Jones,et al.  Maximum Likelihood Fitting of ARMA Models to Time Series With Missing Observations , 1980 .

[17]  C. J. Stone,et al.  Asymptotic Properties of Estimators of a Location Parameter , 1974 .

[18]  E. Hannan,et al.  Vector linear time series models: corrections and extensions , 1978, Advances in Applied Probability.

[19]  A. M. Walker.  Some consequences of superimposed error in time series analysis , 1960 .

[20]  M. Otto,et al.  Outliers in Time Series , 1972 .

[21]  W. S. Krasker.  Estimation in Linear Regression Models with Disparate Data Points , 1980 .

[22]  F. Hampel.  Contributions to the theory of robust estimation , 1968 .

[23]  Emanuel Parzen,et al.  Efficient Estimation of Stationary Time Series Mixed Schemes. , 1971 .

[24]  R. Martin,et al.  Robust bayesian estimation for the linear model and robustifying the Kalman filter , 1977 .

[25]  George E. P. Box,et al.  Intervention Analysis with Applications to Economic and Environmental Problems , 1975 .

[26]  E. Handschin,et al.  Bad data analysis for power system state estimation , 1975, IEEE Transactions on Power Apparatus and Systems.

[27]  W. Dunsmuir.  A Central Limit Theorem for Parameter Estimation in Stationary Vector Time Series and its Application to Models for a Signal Observed with Noise , 1979 .

[28]  F. Hampel.  Robust estimation: A condensed partial survey , 1973 .

[29]  E. Wegman,et al.  A Monte Carlo Study of Robust Estimators of Location , 1977 .

[30]  R. Gray,et al.  Robustness of Estimators on Stationary Observations , 1979 .

[31]  Colin L. Mallows,et al.  Two Diagnostic Displays for Robust Regression Analysis , 1977 .

[32]  I. Konvalinka,et al.  Simultaneous estimation of poles and zeros in speech analysis and ITIF-iterative inverse filtering algorithm , 1979 .

[33]  P. Whittle,et al.  Estimation and information in stationary time series , 1953 .

[34]  D. Thomson,et al.  Robust Estimation of Power Spectra , 1979 .

[35]  J. Durbin.  EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[36]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .