AI 中文总结
研究在时间序列分析中自相关函数的估计问题，提出基于观测值比率的三种稳健估计量，推导其渐近分布，经蒙特卡罗模拟分析有限样本性质，结果表明所提估计量在有异常值时稳健，估计高阶自相关时性能优于基于秩的估计量。
AI 中文摘要
在时间序列分析中，对自相关函数进行充分估计至关重要。本文提出了三种基于观测值比率的稳健估计量，它们对异常值具有很强的抵抗力。第一个基于中位数的估计量效率不高，第二个是具有更好效率特性的拟最大似然（QML）估计量。第三个是插件估计量，计算简单，效率与最大似然估计量相似。推导了前两个估计量在真实自相关为零时的渐近分布，表明插件估计量的渐近分布与QML估计量相近，可用于推断。通过蒙特卡罗模拟分析了所提估计量的有限样本性质，并与样本自相关和基于秩的现有稳健估计量进行比较。结果表明，所提估计量在无异常值时方差比样本自相关大，但在有异常值时高度稳健，在估计大于一阶的自相关时比基于秩的流行稳健估计量性能更好。通过估计西班牙IBEX35指数日收益率、美国季度经济增长和美国月度通胀的相关图说明了结果。
英文摘要
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.
