论文标题
小样本时间序列的光谱方法：完整的期刊方法
Spectral methods for small sample time series: A complete periodogram approach
论文作者
论文摘要
期刊图是一种广泛用于分析二阶固定时间序列的工具。期刊图的一个有吸引力的特征是期刊的期望大致等于时间序列的基础光谱密度。但是，这只是一个近似值，众所周知，周期图具有有限的样品偏差，在小样本中可能很严重。在本文中，我们表明，由于在期刊构建中使用的离散傅立叶变换之一中观察的有限边界而产生的偏差。此外，我们表明，通过在观察边界上使用时间序列的最佳线性预测指标，我们可以获得一个“完整的周期图”，该图是光谱密度的无偏估计器。实际上，由于最佳的线性预测因子未知，因此无法评估“完整的期刊”。我们提出了一种估计最佳线性预测指标的方法，并证明所得的“估计的完整期刊”的偏差小于常规期间图。估计的完整周期图和锥形版本用于估计参数，可以用集成的光谱密度表示。我们证明，所得估计器的偏差比常规周期图对应物要小。提出的方法用仿真和真实数据说明。
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time series. However, this is only an approximation, and it is well known that the periodogram has a finite sample bias, which can be severe in small samples. In this paper, we show that the bias arises because of the finite boundary of observation in one of the discrete Fourier transforms which is used in the construction of the periodogram. Moreover, we show that by using the best linear predictors of the time series over the boundary of observation we can obtain a "complete periodogram" that is an unbiased estimator of the spectral density. In practice, the "complete periodogram" cannot be evaluated as the best linear predictors are unknown. We propose a method for estimating the best linear predictors and prove that the resulting "estimated complete periodogram" has a smaller bias than the regular periodogram. The estimated complete periodogram and a tapered version of it are used to estimate parameters, which can be represented in terms of the integrated spectral density. We prove that the resulting estimators have a smaller bias than their regular periodogram counterparts. The proposed method is illustrated with simulations and real data.
