Abstract
A practical method is developed for outlier detection in autoregressive modelling. It has the interpretation of a Mahalanobis distance function and requires minimal additional computation once a model is fitted. It can be of use to detect both innovation outliers and additive outliers. Both simulated data and real data re used for illustration, including one data set from water resources.
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References
Belsley, D.A.; Kuh, E.; Welsch, R.E. 1980: Regression diagnostics. New York: Wiley
Box, G.E.P.; Jenkins, G.M. 1970: Time series analysis: Forecasting and control. San Franciso: Holden-Day
Brockwell, P.J.; Davis, R.A. 1987: Time series: Theory and methods. New York: Springer-Verlag
Brubacher, S.R. 1974: Time series outlier detection and modeling with interpolation. Bell Laboratories Technical Memo
Cook, R.D.; Weisberg, S. 1982: Residuals and influence in regression. London: Chapman and Hall
Elton, C.; Nicholson, M. 1942: The ten-year cycle in numbers of the LYNX in Canada. J. Anim. Ecol. 11, 215–244.
Fox, A.J. 1972: Outliers in time series. J. Roy. Statist. Soc., B 34, 3, 350–363
Hipel, K.W.; Mcleod, A.I. 1978: Preservation of the rescaled adjusted range 2. Simulation studies using Box-Jenkins models. Water Resources Research 14, 509–516
Hoaglin, D.C.; Welsch, R. 1978: The hat matrix in regression and ANOVA. Amer. Statistician 32, 17–22
Huber, P. 1981: Robust statistics. New York: Wiley
Kleiner, B.; Martin, R.D.; Thomson, D.J. 1979: Robust estimation of power spectra. J. Roy. Statist. Soc., B 41, 313–351
Kunsch, H. 1984: Infinitesimal robustness for autoregressive processes. Annals of Statistics 12, 843–855
Lawson, C.R.; R.J. Hanson 1974: Solving least-square problems. Englewood Cliffs, N.J.: Prentice-Hall
Mann, H.B.; Wald, A. 1943: On the statistical treatment of linear stochastic difference equations. Econometrica 11, 173–221
Martin, R.D. 1980: Robust methods for time series. In: Findley, D.E. (Ed.) Applied time series. New York: Academic Press
Martin, R.D. 1983: Robust-resistant spectral analysis. In Brillinger, P.R.; Krishnaiah, P.R. (Eds.) Time series in the frequency domain, handbook of statistics 3. North-Holland
Martin, R.D.; Samarov, A.; Vandaele, W. 1982: Robust method for ARMIA models. Tech. Report. No. 21, Department of Statistics, University of Washington, Seattle
Martin, R.D.; Zeh, J.E. 1977: Determining the character of time series outliers. Proceedings of the Amer. Statist. Assoc., Business and Economics Section
Thomas, H.A.; Fiering, M.B. 1962: Mathematical synthesis of stream flow sequences for the analysis of river basins by simulation. In: Maass et al. (Eds.) Design of Water Resources. Harvard University Press
Tong, H. 1978: On a threshold model. In: Chan, C.H. (Ed.) Pattern recognition and signal processing. Netherlands: Sythoff and Noordhoff
Tong, H. 1983: Threshold models in non-linear time series analysis. New York: Springer-Verlag
Tong, H. 1987: Non-linear time series models of regularly sampled data: A review in proceedings of the first world congress of the Bernoulli society of mathematical statistics and probability, held in Sept. 1986 at Tashkent, USSR. Vol. 2, pp. 355–367, VNU science press, Netherlands
Tong, H.; Lim, K.S. 1980: Threshold autoregression, limit cycles and cyclical data (with discussion). J. Roy. Stat. Soc. 13, 42, 245–292
Velleman, P.; Welsch, R. 1981: Efficient computing of regression diagnostics. Amer. Statistician 35, 234–42
Yevjevich, V.M. 1963: Fluctuation of wet and dry years 1, research data assembly and mathematical modesl. Hydrological Papers Colorado State University, Fort Collins, Colorado
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Hau, M.C., Tong, H. A practical method for outlier detection in autoregressive time series modelling. Stochastic Hydrol Hydraul 3, 241–260 (1989). https://doi.org/10.1007/BF01543459
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DOI: https://doi.org/10.1007/BF01543459