Pseudo-maximum likelihood estimation of ARCH(∞) models

• 成果类型: Article
• 署名作者: Robinson, Peter M.; Zaffaroni, Paolo
• 署名单位: University of London; London School Economics & Political Science; Imperial College London
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000245
• 发表日期: 2006
• 页码: 1049-1074
• 关键词: autoregressive conditional heteroskedasticity; garch processes; ASYMPTOTIC THEORY; ARCH models; stochastic volatility; Whittle Estimation; long memory; stationarity; Consistency; returns

摘要

Strong consistency and asymptotic normality of the Gaussian pseudomaximum likelihood estimate of the parameters in a wide class of ARCH(infinity) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particular parameterizations are discussed.