Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter

• 作者: Andrew Bartlett William McCormick
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: NONNEGATIVE Time Series AUTOREGRESSIVE PROCESSES Extreme Value ESTIMATOR Regular Variation Point PROCESSES
• 年，卷（期）: 2012,（12）
• 页码范围: 2133-2147
• 页数: 15页
• 分类号: O1

摘要

Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.