Serial correlation of detrended time series.
Serial correlation of detrended time series.
复制标题
去趋势时间序列的序列相关性。
DOI：
10.1103/physreve.78.036707
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Craciun
中科院分区：
文献类型：
--
作者：
C. Vamos;M. Craciun
时间序列分析中一个基本的初步步骤是将确定性成分与随机成分分离。如果信号是噪声叠加在确定性趋势上的结果，则第一个信号必须估计并从信号中去除趋势，以获得平稳随机分量的估计。伴随估计趋势的误差也以去趋势误差的形式传递给估计噪声。因此，去趋势后得到的噪声参数的估计器的统计误差大于单独考虑的噪声的统计误差特征。本文用蒙特卡罗方法研究去趋势误差，该方法基于自动数值算法，用于生成非单调趋势和构造与主观方法相同的估计多项式趋势。对于一阶自回归噪声，我们证明了用自协方差函数和自相关函数估计的噪声参数的平均去趋势误差与噪声固有的统计误差几乎不相关，并且它们具有可比较的幅度。对于具有显着趋势的实际时间序列，我们讨论了一种计算去趋势后估计参数误差的递推方法，证明了去趋势误差大于总误差的一半。
A preliminary essential procedure in time series analysis is the separation of the deterministic component from the random one. If the signal is the result of superposing a noise over a deterministic trend, then the first one must estimate and remove the trend from the signal to obtain an estimation of the stationary random component. The errors accompanying the estimated trend are conveyed as well to the estimated noise, taking the form of detrending errors. Therefore the statistical errors of the estimators of the noise parameters obtained after detrending are larger than the statistical errors characteristic to the noise considered separately. In this paper we study the detrending errors by means of a Monte Carlo method based on automatic numerical algorithms for nonmonotonic trends generation and for construction of estimated polynomial trends alike to those obtained by subjective methods. For a first order autoregressive noise we show that in average the detrending errors of the noise parameters evaluated by means of the autocovariance and autocorrelation function are almost uncorrelated to the statistical errors intrinsic to the noise and they have comparable magnitude. For a real time series with significant trend we discuss a recursive method for computing the errors of the estimated parameters after detrending and we show that the detrending error is larger than the half of the total error.
影响因子：
2.4
作者：
Chen, Z;Hu, K;Ivanov, PC
通讯作者：
Ivanov, PC
影响因子：
2.4
作者：
Hu, K;Ivanov, PC;Stanley, HE
通讯作者：
Stanley, HE
影响因子：
2.4
作者：
Carbone, A;Castelli, G;Stanley, HE
通讯作者：
Stanley, HE