Robust estimation of the autocorrelation function via forward ratios
通过前向比值稳健估计自相关函数AI 解读 ↓
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通过前向比值稳健估计自相关函数
- 研究问题
- 如何在异常值存在时稳健估计时间序列自相关函数，并在统计效率、计算便利与推断可用性之间取得平衡？
- 方法与思路
- 作者基于观测比值提出中位数、准最大似然及免优化的代入估计量，并分析部分渐近分布、显著性带与模拟表现。
- 材料陈述的贡献
- 摘要称方法牺牲无污染样本中的部分效率以提高抗异常值能力，在高阶自相关估计中优于所比较的秩方法。
- 阅读关注点
- 应核对零值与比值异常的处理、零自相关下渐近结果的条件，以及代入近似和逐点显著性带在其他情形中的有效性。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；部分理论限于真自相关为零，摘要未说明更一般情形的推断保证。
原文摘要
It is obvious to say that an adequate estimation of the autocorrelation function is central in time series analysis. In this paper, we propose three new robust estimators based on ratios of observations, which offer strong resistance against outliers. While the first estimator, which is based on the median, is not efficient, the second is a Quasi Maximum Likelihood (QML) estimator with better efficiency properties. The third estimator is a plug-in estimator, which does not require numerical optimization and, consequently, is extremely simple from a computationally point of view, having similar efficiency to that of the ML estimator. We derive the asymptotic distribution of the first two estimators, when the true autocorrelations are zero. Furthermore, we also show that the asymptotic distribution of the plug-in estimator is rather close to that of the QML estimator, allowing for inference and, in particular, for the construction of point-wise significance bands for the autocorrelations. Using Monte Carlo simulations, we analyse the finite sample properties of the proposed estimators and compare them with those of the sample autocorrelations and alternative extant robust estimators based on ranks. Although the proposed estimators have larger dispersion than the sample autocorrelations in uncontaminated time series, they are highly robust in the presence of outliers. Also, they have better properties than popular alternative robust estimators based on ranks when estimating autocorrelations of order larger than one. The results are illustrated by estimating the correlogram of daily IBEX35 returns, quarterly US economic growth and monthly US inflation.