Robust M-estimates and generalized M-estimates for autoregressive parameter estimation

The problem of robust estimation of autoregressive parameters in the presence of outliers is considered. The least squares estimate lacks efficiency robustness when innovation outliers are present. Several M-estimates (maximum likelihood type) corresponding to different cost functions show good efficiency robustness against innovation outliers. The M-estimate with Welsch cost function is found to be the best in a comparative simulation study. However, in the case of additive outliers, M-estimates are not robust and they give large bias errors. Generalized M-estimates are recommended for the additive outlier case. A simulation study shows that a combination of Welsch function as the weight function and Andrews or Welsch function as the cost function produces the best performance in generalized M-estimates