Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

• 成果类型: Article
• 署名作者: Dahlhaus, Rainer; Polonik, Wolfgang
• 署名单位: Ruprecht Karls University Heidelberg; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000867
• 发表日期: 2006
• 页码: 2790-2824
• 关键词: minimum contrast estimators; time-series; CONVERGENCE; models; rates

摘要

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As an example, autoregressive model fitting with a monotonic variance function is discussed in detail, including algorithmic considerations. A key technical tool is the time-varying empirical spectral process indexed by functions. For this process, a Bernstein-type exponential inequality and a central limit theorem are derived. These results for empirical spectral processes are of independent interest.