Highly efficient weighted for autoregression wilcoxon estimes for autoregression

Abstract

In this paper we explore the use of Schweppe-type weights for a class of weighted Wiicoxon estimates and apply the corresponding estimates to an autoregressive time series model This special class of estimates is essentially the autoregressive analog of the HBR-estimates proposed by Chang et al. (1999) in the linear regression context. Assuming a stationary finite second moment autoregressive model of order p, asymptotic linearity properties are derived for the HBR-estimate. Based on these properties, the HBR-estimate is shown to be asymptotically normal at rate nl/2. Tests of general linear hypotheses as well as standard errors for confidence interval procedures can be based on such results. In a linear regression setting, the HBR-estimate is highly efficient and inherits a totally bounded influence function and a 50percent breakdown point. Examples and a Monte Carlo study over innovated and additive outlier models indicate that these properties of the HBR-estimate are preserved in an autoregressive time series context, Thus, the HBR-estimate provides a highly efficient and robust alternative for autoregressive time series estimation.

Keywords:

• Additive outliers
• Autoregressive time series
• Innovation outliers
• High-breakdown estimates
• Rank-based estimates
• Schweppe weights
• Wiicoxon estimates