几乎周期相关时间序列谱分析中的渐近分布和子采样

周期相关随机过程的极小极大估计问题

Minimax Estimation Problem for Periodically Correlated Stochastic Processes

本文研究周期相关随机过程线性泛函的最优线性估计问题，给出谱密度已知和未知两类场景下估计的均方误差与谱特性计算公式，并推导最不利谱密度及极小极大鲁棒谱特性的确定公式。

带噪声观测的具有周期相关增量的连续时间随机过程的预测问题

Prediction problem for continuous time stochastic processes with periodically correlated increments observed with noise

本文研究了带周期平稳噪声观测下具有周期相关增量的连续时间随机过程的线性泛函均方最优估计问题，通过变换为无限维向量平稳序列，给出了最优估计的谱特性、误差公式及极小极大稳健谱特性。

具有周期相关增量的连续时间随机过程的估计问题

Estimation problem for continuous time stochastic processes with periodically correlated increments

本文针对具有周期相关增量的连续时间随机过程，通过构造无穷维向量平稳增量序列，推导线性泛函最优估计的均方误差、谱特征及极小极大稳健公式。

Minimax extrapolation problem for periodically correlated stochastic sequences with missing observations

The problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence $ζ(j)$ from observations of the sequence $ζ(j)+θ(j)$ at points $j\in\{\dots,-n,\dots,-2,-1,0\}\setminus S$, $S=\bigcup _{l=1}^{s-1}\{-M_l\cdot T+1,\dots,-M_{l-1}\cdot T-N_{l}\cdot T\}$, is considered, where $θ(j)$ is an uncorrelated with $ζ(j)$ periodically correlated stochastic sequence. Formulas for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional $Aζ$ are proposed in the case where spectral …

连续时间周期相关各向同性随机场的外推问题

Extrapolation Problem for Continuous Time Periodically Correlated Isotropic Random Fields

本文研究了连续时间周期相关各向同性随机场泛函的最优线性估计问题，在谱密度精确已知和未精确已知两种情形下，分别推导了均方误差与谱特征计算公式及极小化极大稳健估计公式。

连续时间周期相关各向同性随机场的滤波

Filtering of Continuous Time Periodically Correlated Isotropic Random Fields

本文研究连续时间周期相关各向同性随机场的最优线性滤波问题，在谱确定与谱不确定情形下分别推导了均方误差与谱特征公式，并提出了极小极大稳健估计方法。

球面上各向同性且周期相关的随机场的估计

Estimation of periodically correlated random fields that are isotropic on a sphere

研究球面上周期相关随机场线性估计问题，提出已知和未知谱密度矩阵下的最优估计与极小极大稳健估计公式。

Estimation of the asymptotic variance of univariate and multivariate random fields and statistical inference

Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance which adds up all autocovariances in the temporal and spatial domain. Especially, it arises in the standardization of test statistics based on partial sums of random fields and thus the construction of tests requires its estimation. In this paper we propose consistent estimators for this parameter for strictly stationary ϕ-mixing random fields with arbitrary dim…

带噪声观测的具有周期相关增量的连续时间随机过程的极小极大插值

Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise

本文研究带周期平稳噪声观测下具有周期平稳增量的连续时间随机过程缺失值线性泛函的最优估计问题，通过构造平稳增量序列，在已知谱密度和给定可容许谱密度集合两种情形下分别给出了最优估计及极小极大稳健谱特征的计算公式。

Continuous-time GARCH process driven by semi-Lévy process

In this paper we study the simple semi-Lévy driven continuous-time generalized autoregressive conditionally heteroscedastic (SS-COGARCH) process. The statistical properties of this process are characterized. This process has the potential to approximate any semi-Lévy driven COGARCH processes. We show that the state representation of such SS-COGARCH process can be described by a random recurrence equation with periodic random coefficients. The almost sure absolute convergence of the state process is proved. The periodically stationary solution of the state process is shown which cause the volat…

具有非平稳外生变量的部分线性模型的估计与预测

Estimating and forecasting partially linear models with non stationary exogeneous variables

本文提出了一种具有异方差输入噪声和外生变量的周期相关部分线性模型的Backfitting估计和预测方法。给出了估计量的一个收敛速率。即使周期未知，结果也有效。

评估可变带通周期块自举法的偏差

Assessing Bias in the Variable Bandpass Periodic Block Bootstrap Method

针对可变带通周期块自举法（VBPBB）估计抽样分布偏差未被检验的问题，本研究在不同复杂度周期相关时间序列模型中探究其整体平均与逐点平均偏差，通过R模拟分析，为方法有效性提供见解并给出实施建议与理论方向。

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated.

具有周期和概周期结构的非平稳时间序列滑动块自举法的一致性及应用

Consistency and application of moving block bootstrap for non-stationary time series with periodic and almost periodic structure

本文的目的是建立具有周期和概周期结构的非平稳时间序列的滑动块自举一致性的充分条件。研究的参数是期望函数的平均值。一致性在相当一般的情况下成立：如果所有的联合分布的系列是周期性的，那么它足以假设中心极限定理和强混合性质，连同可求和的自协方差函数。在平均函数几乎是周期性的情况下，我们还需要根统计量的四阶矩的一致有界性。结果表明，这些理论结果可用于周期（PC）和几乎周期（APC）相关时间序列的傅里叶系数的统计推断。一个模拟的例子显示了如何使用一个图形诊断测试的显着频率和平稳性在这些类的时间序列。