Limit theory for the sample autocorrelations and extremes of a GARCH (1,1) process

• 成果类型: Article
• 署名作者: Mikosch, T; Starica, C
• 署名单位: University of Groningen; Chalmers University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1427-1451
• 关键词: adjustment coefficient; difference equation; point process; stationarity; ARCH; CONVERGENCE; variance; BEHAVIOR; MODEL

摘要

The asymptotic theory for the sample autocorrelations and extremes of a GARCH(I, 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to 1, that is, when one is close to an infinite Variance marginal distribution. This situation has been observed for various financial log-return series and led to the introduction of the IGARCH model. In such a situation, the sample autocorrelations are unreliable estimators of their deterministic counterparts for the time series and its absolute values, and the sample autocorrelations of the squared time series have nondegenerate limit distributions. We discuss the consequences for a foreign exchange rate series.