Journal of the American Statistical Association · 1979 · 70 citations · 0 references
BusinessData ScienceEconometricsForecastingTime Series AnalysisMaximum Likelihood EstimationRobust Statistical ModelingRobust StatisticsTime Series EconometricsTime Series ForecastingTime Series ModelingAutoregressive ModelsAutoregressive ProcessesAutoregressive Time Series ModelsRobust EstimationRobust Parameter EstimationRobust RegressionRobust Time Series AnalysisRobust Time Series Estimation
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.