Time series regression models with locally stationary disturbance
Time series regression models with locally stationary disturbance
复制标题
具有局部平稳扰动的时间序列回归模型
DOI：
10.1007/s11203-017-9155-7
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
Junichi Hirukawa
中科院分区：
文献类型：
--
作者：
長谷川洋平;甲藤二郎;Junichi Hirukawa
具有平稳残差的时间序列线性回归模型是一个被广泛研究的课题，并在许多领域得到了广泛的应用。然而，对残差的平稳性假设似乎是限制性的。对可能包含光谱变化的相对较长的时间序列数据的分析在许多领域都是有意义的。局部平稳过程具有随时间变化的谱密度，其结构随时间平滑变化。因此，我们将模型推广到局部平稳残差的情况。回归系数向量的最佳线性无偏估计（BLUE）涉及残差协方差矩阵，而残差协方差矩阵通常是未知的。因此，我们经常使用最小二乘估计器（LSE），它总是可行的，但通常效率不高。我们计算了BLUE和LSE的渐近协方差矩阵。我们还研究了LSE相对于BLUE的效率。数值例子说明了局部平稳扰动下的情况。
Time series linear regression models with stationary residuals are a well studied topic, and have been widely applied in a number of fields. However, the stationarity assumption on the residuals seems to be restrictive. The analysis of relatively long stretches of time series data that may contain changes in the spectrum is of interest in many areas. Locally stationary processes have time-varying spectral densities, the structure of which smoothly changes in time. Therefore, we extend the model to the case of locally stationary residuals. The best linear unbiased estimator (BLUE) of vector of regression coefficients involves the residual covariance matrix which is usually unknown. Hence, we often use the least squares estimator (LSE), which is always feasible, but in general is not efficient. We evaluate the asymptotic covariance matrices of the BLUE and the LSE. We also study the efficiency of the LSE relative to the BLUE. Numerical examples illustrate the situation under locally stationary disturbances.