Nonparametric and Robust Approach in Time Series Analysis

研究了平稳高斯过程在不假定特定参数模型的情况下，用非参数稳健方法估计其自相关性，以及时间序列分析中基于非参数谱估计的检验问题，讨论了具有无限滑动平均表示的平稳高斯过程的基于极限估计函数的自相关估计问题。提出了几种新的估计量，并得到了它们的渐近分布。讨论了具有加性异常值的平稳高斯过程的自相关估计问题。比较了几种基于限幅估计函数的自相关估计器的偏差，我们考虑检验合适的谱密度函数的积分是否等于给定的常数。针对这一问题，提出了一种基于非参数谱估计的检验方法，并给出了非参数连续方案序列下的渐近功率估计。我们讨论了一个过程的谱密度的适当函数的积分是否等于另一个过程的谱密度函数的积分。

This research is concerned with the estimation of the autocorrelation of a stationary Gaussian process by nonparametric and robust method without assuming a specific parametric model, and the tests based on nonparametric spectral estimators in time series analysis.We discuss the estimation of the autocorrelation based on limiter estimating functions for a stationary Gaussian process having the representation of an infinite moving average. Several new estimators are proposed and their asymptotic distributions are obtained. The estimation of the autocorrelation of a stationary Gaussian process with additive outliers is discussed. The biases of several estimators of the autocorrelation based on limiter estimating functions are compared.We consider to test whether the integral of appropriate function of the spectral density is equal to a given constant or not. For this problem a test based on a nonparametric spectral estimator is proposed, and the asymptotic power evaluation under a sequence of nonparametric contiguous alternatives is given. We discuss to test whether the integral of appropriate function of the spectral density of a process, is equal to that of the other process, or not.