论文标题
基于模型的偏差校正短AR（1）和AR（2）过程
Model-based bias correction for short AR(1) and AR(2) processes
论文作者
论文摘要
自回旋（AR）过程的类别广泛用于模拟观察到的时间序列中的时间依赖性。此类模型很容易获得，并使用可自由获得的统计软件（例如R.）进行了常规拟合。分析短时间序列中的潜在警告是，AR过程系数的常用估计量严重偏差。本文提出了一种基于模型的方法来校正一阶和二阶AR过程系数的众所周知估计器，从而考虑了原始估计器的采样分布。这是通过使用加权正交多项式回归对真实和估计的AR系数之间的关系来实现的，并适合大量模拟。新估计量的有限样本分布使用偏差密度的转换来近似，并通过模拟和对真实生态数据集的分析来证明它们的性质。在我们随附的R包装arbiasCorcect中，新的估计器可轻松获得长度n = 10、11，...，... 50的时间序列，其中使用精确或有条件的最大可能性，Burg的方法或Yule-Walker方程发现了原始估计。
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential caveat in analyzing short time series is that commonly applied estimators for the coefficients of AR processes are severely biased. This paper suggests a model-based approach for bias correction of well-known estimators for the coefficients of first and second-order stationary AR processes, taking the sampling distribution of the original estimator into account. This is achieved by modeling the relationship between the true and estimated AR coefficients using weighted orthogonal polynomial regression, fitted to a huge number of simulations. The finite-sample distributions of the new estimators are approximated using transformations of skew-normal densities and their properties are demonstrated by simulations and in the analysis of a real ecological data set. The new estimators are easily available in our accompanying R-package ARbiascorrect for time series of length n = 10, 11, ... , 50, where original estimates are found using exact or conditional maximum likelihood, Burg's method or the Yule-Walker equations.
