ESTIMATION OF TIME SERIES MODELS USING RESIDUALS DEPENDENCE MEASURES

• 成果类型: Article
• 署名作者: Velasco, Carlos
• 署名单位: Universidad Carlos III de Madrid
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2220
• 发表日期: 2022
• 页码: 3039-3063
• 关键词: EMPIRICAL CHARACTERISTIC FUNCTION; maximum-likelihood-estimation; generalized spectral tests; Adaptive estimation; phase; INDEPENDENCE

摘要

We propose new estimation methods for time series models, possibly noncausal and/or noninvertible, using serial dependence information from the characteristic function of model residuals. This allows to impose the i.i.d. or martingale difference assumptions on the model errors to identify the unknown location of the roots of the lag polynomials for ARMA models without resorting to higher order moments or distributional assumptions. We consider generalized spectral density and cumulative distribution functions to measure residuals dependence at an increasing number of lags under both assumptions and discuss robust inference to higher order dependence when only mean independence is imposed on model errors. We study the consistency and asymptotic distribution of parameter estimates and discuss efficiency when different restrictions on error dependence are used simultaneously, including serial uncorrelation. Optimal weighting of continuous moment conditions yields maximum likelihood efficiency under independence for unknown error distribution. We investigate numerical implementation and finite sample properties of the new classes of estimates.