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长记忆模型的代入估计
- 研究问题
- 在均值未知的高斯 ARFIMA 模型中，将均值估计值代入似然后，为何仍可能出现常规最大似然所没有的二阶偏差？
- 方法与思路
- 作者对代入最大似然和 Whittle 最大似然作渐近展开，追踪 Bartlett 恒等式失效产生的偏差项，并考察 ARFIMA 特例。
- 材料陈述的贡献
- 摘要称二阶偏差中存在额外项，其来源是第一 Bartlett 恒等式失效；作者认为这似乎解释了既有模拟观察到的偏差。
- 阅读关注点
- 读全文应核对均值估计的收敛要求、长记忆参数范围、展开余项与额外偏差项，并区分本文推导和所引用的模拟结果。
- 阅读边界
- 仅据所给 RePEc 出版社摘要，部分公式已缺失，不能重建完整信息矩阵或似然表达式，也不能确定偏差结论的普遍范围。
原文摘要
We consider the Gaussian ARFIMA(j,d,l) model, with spectral density and an unknown mean . For this class of models, the n−1-normalized information matrix of the full parameter vector, (μ,θ), is asymptotically degenerate. To estimate θ, Dahlhaus (1989, Annals of Statistics 17, 1749–1766) suggested using the maximizer of the plug-in log-likelihood, , where is any n(1−2d)/2-consistent estimator of μ. The resulting estimator is a plug-in maximum likelihood estimator (PMLE). This estimator is asymptotically normal, efficient, and consistent, but in finite samples it has some serious drawbacks. Primarily, none of the Bartlett identities associated with are satisfied for fixed n. Cheung and Diebold (1994, Journal of Econometrics 62, 301–316) conducted a Monte Carlo simulation study and reported that the bias of the PMLE is about 3–4 times the bias of the regular maximum likelihood estimator (MLE). In this paper, we derive asymptotic expansions for the PMLE and show that its second-order bias is contaminated by an additional term, which does not exist in regular cases. This term arises because of the failure of the first Bartlett identity to hold and seems to explain Cheung and Diebold's simulated results. We derive similar expansions for the Whittle MLE, which is another estimator tacitly using the plug-in principle. An application to the ARFIMA(0,d,0) shows that the additional bias terms are considerable.Research on this topic commenced during 2000–2002, while the author was visiting the Cowles Foundation for Research in Economics at Yale University. The author is most grateful to the Cowles Foundation for their generous hospitality and to Donald Andrews and Peter Phillips for numerous helpful comments.