Robust Estimation of the First-Order Autoregressive Parameter
- 1 March 1979
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 74 (365) , 140
- https://doi.org/10.2307/2286743
Abstract
Outliers in time series can adversely affect both the least squares estimates and ordinary M-estimates of autoregressive parameters. Attention is focused here on obtaining robust estimates of the parameter for a first-order autoregressive time series xk The observations are y k = z k + v k, and two models are considered: Model IO, with v k ≡ 0, x k possibly non-Gaussian, and Model AO, with v k nonzero and possibly quite large a small fraction of the time, and x k Gaussian. A class of generalized M-estimates is proposed which has attractive mean-squared-error robustness properties towards both IO and AO type deviations from the Gaussian model.Keywords
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