Whittle Likelihood Estimation of Nonlinear Autoregressive Models With Moving Average Residuals

• 成果类型: Article
• 署名作者: Wang, Tianhao; Xia, Yingcun
• 署名单位: National University of Singapore; National University of Singapore; University of Electronic Science & Technology of China
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.946513
• 发表日期: 2015
• 页码: 1083-1099
• 关键词: time-series models

摘要

The Whittle likelihood estimation (WLE) has played a fundamental role in the development of both theory and computation of time series analysis. However, WLE is only applicable to models whose theoretical spectral density function (SDF) is known up to the parameters in the models. In this article, we propose a residual-based WLE, called extended WLE (XWLE), which can estimate models with their SDFs only partially available, including many popular time series models with correlated residuals. Asymptotic properties of XWLE are established. In particular, XWLE is asymptotically equivalent to WLE in estimating linear ARMA models, and is also capable of estimating nonlinear AR models with MA residuals and even with exogenous variables. The finite-sample performances of XWLE are checked by simulated examples and real data analysis.