Rank-based estimation for all-pass time series models

• 成果类型: Article
• 署名作者: Andrews, Beth; Davis, Richard A.; Breidt, F. Jay
• 署名单位: Northwestern University; Colorado State University System; Colorado State University Fort Collins
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001316
• 发表日期: 2007
• 页码: 844-869
• 关键词: r-estimation; likelihood-estimation; arma models; autoregression; systems

摘要

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449-1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.