Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models

• 成果类型: Article
• 署名作者: Truquet, Lionel
• 署名单位: Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12221
• 发表日期: 2017
• 页码: 1391-1414
• 关键词: series; nonstationarities

摘要

We develop a complete methodology for detecting time varying or non-time-varying parameters in auto-regressive conditional heteroscedasticity (ARCH) processes. For this, we estimate and test various semiparametric versions of time varying ARCH models which include two well-known non-stationary ARCH-type models introduced in the econometrics literature. Using kernel estimation, we show that non-time-varying parameters can be estimated at the usual parametric rate of convergence and, for Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non-time-varying parameters or for testing the second-order dynamics. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.