FREQUENCY DOMAIN MINIMUM DISTANCE INFERENCE FOR POSSIBLY NONINVERTIBLE AND NONCAUSAL ARMA MODELS

• 成果类型: Article
• 署名作者: Velasco, Carlos; Lobato, Ignacio N.
• 署名单位: Universidad Carlos III de Madrid; Instituto Tecnologico Autonomo de Mexico
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1560
• 发表日期: 2018
• 页码: 555-579
• 关键词: moving average processes; time-series models; likelihood-estimation; identification; INFORMATION

摘要

This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments. Contrary to existing estimators, the proposed one is consistent under general assumptions, and may improve on the efficiency of estimators based on only second order moments. Our procedures are also applicable for processes for which either the third or the fourth order spectral density is the zero function.