On consistency of the likelihood moment estimators for a linear process with regularly varying innovations

基于经验特征函数方法的具有稳定新息的季节性分数阶ARIMA估计

Estimation for seasonal fractional ARIMA with stable innovations via the empirical characteristic function method

最大似然法虽然被广泛使用，但由于模型所依据的假设与观测数据的真实密度概率分布之间的不一致，可能是不稳健的。由于经验特征函数是经验分布函数的傅里叶变换，因此它保留了样本中的所有信息，但可以克服似然带来的困难。本文讨论了稳定季节分数ARIMA过程的ECF估计方法。在一定的假设下，我们证明了所得到的估计是一致的，渐近正态分布。为了比较的目的，我们还考虑了Ndongo等人（2010）开发的MCMC Whittle方法。这两种方法的性能进行了讨论，使用Monte Carlo模拟。

Developments in Maximum Likelihood Unit Root Tests

The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic distribution of this test statistic that is simpler and more direct than the previous method. The response surface regression method is used to obtain a fast algorithm that computes accurate finite-sample critical values. This algorithm is available in the R package {\tt mleur} that is available on CRAN. The empirical power of the new test is shown to be much …

用基于残差的统计量检验几乎非平稳过程中的流行病变化

Testing epidemic change in nearly nonstationary process with statistics based on residuals

本文研究了一阶自回归过程$ y_{n,k} = φ_n y_{n,k-1} + ε_{k} + a_{n,k}$的新息的传染型变化，其中$ϕ_n$是$(-1,1)$中的常数或$(0,1)$中的序列，收敛到1。对于在某个未知区间$\mathbb{I}_n^\ast=(k^\ast,k^\ast+\ell^\ast]$内的$k$，$a_{n,k}=a_n$，而对于在$\mathbb{I}_n^\ast$外的$k$，$a_{n,k}=0$。当$a_n\neq 0$，我们有一个流行病偏离通常（零）的平均创新。由于没有观察到新息，我们建立均匀增量统计过程$y_{n,k}$的残差$(\widehatε_k)$。我们假设新息$(ε_k)$随指标$p \ge 2$有规律地变化，或者满足可积性条件：对于$p > 2$满足$\lim_{t \to \infty} t^p P(|ε_1| > t) = 0$，对于$p=2$满足$Eε_k^2 < \infty$.我们发现极限分布的测试下没有变化，并证明一致性短期流行病是$\ell^\ast=O(n^β)$的一些$0<β\le 1/2$。

Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination

Consider a multivariate Lévy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving Lévy process is from a parametric family. We derive the likelihood function assuming that the innovation term is absolutely continuous. Two examples are studied in detail: the process where the stationary distribution or background driving Lévy process is given by a weak variance alpha-gamma process, which is a multivariate generalisation of the variance gamma process created using weak subordination. In the former case, we give an explicit representation of the background dri…

线性过程的精确中偏差和大偏差

Exact Moderate and Large Deviations for Linear Processes

大中偏差概率在保险、风险分析等许多应用领域中起着重要的作用。本文研究了具有独立新息的线性过程的非对数形式的精确中偏差和大偏差渐近性。我们分析的线性过程是一般的，因此它们包括长记忆的情况。我们给出了一个渐近表示的概率尾部的规范化的总和，并指定的区域中，它可以近似为一个标准正态分布或边缘分布的创新过程。然后将结果应用于回归估计、移动平均、分数积分过程、具有规则变化指数的线性过程和线性过程的函数。我们还考虑了风险理论和金融学中的基本量--在险价值和期望损失的计算。

对称$α$ -稳定过程的经验似然方法

An empirical likelihood approach for symmetric $α$-stable processes

经验似然法是一种非参数统计方法，用于关键未知量的假设检验或置信区域的构造。该方法已应用于独立同分布随机变量和二阶平稳过程的情形。近年来，我们在许多领域观察到重尾数据。为了适当地模拟这样的数据，我们考虑对称标量和多元$α$ -稳定的线性过程所产生的无穷方差的新息序列。我们在经验似然比函数中使用了一个Whittle似然型估计函数，并导出了$α$ -稳定线性过程的经验似然比统计量的渐近分布.经验似然统计方法将二阶平稳过程的估计和检验理论很好地推广到重尾数据分析中，而不是简单地推广到金融统计分析中。

GARCH过程参数估计的有效性

The efficiency of the estimators of the parameters in GARCH processes

本文提出了一类Gestival（p，q）序列参数的估计。我们证明了我们的估计是一致的，渐近正态在温和的条件下。详细讨论了拟极大似然估计和似然估计。我们证明了极大似然估计是最优的。如果新息分布的尾部是多项式的，则即使是基于指数密度的准最大似然估计也比Lee和Hansen和Lumsdaine的基于标准正态密度的准似然估计表现得更好。

Time-varying first-order autoregressive processes with irregular innovations

We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is Hölder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A precise control of this method demands a delicate analysis of extremes of certain weakly dependent processes, our main result being a concentration inequality for such quantities. Based on our analysis, upper and matching minimax lower bounds are derived, showing the optimality of our estimators. Unlike the regular case, the information theoretic complexity depen…

ARCH模型估计的有效性和影响函数

Efficiency and influence function of estimators for ARCH models

本文基于估计函数理论，提出了一类线性回归模型的封闭型最优估计。估计函数（EF）估计器与广泛使用的最大似然（ML）和拟最大似然（QML）估计器相比具有以下优点：（i）它可以容易地实现;（ii）它不依赖于新息的分布假设;（iii）它不需要使用任何数值优化过程或选择条件方差方程的初始值。在正态性的情况下，ML和QML估计量的渐近分布自然是相同的，因此与我们的一致。此外，通过影响函数导出了EF估计器的鲁棒性。仿真结果表明，我们的估计相对于ML和QML估计的效率优势是相当大的一些新息分布。

非平稳随机系数自回归模型的估计

Estimation in nonstationary random coefficient autoregressive models

研究了随机系数自回归模型中参数的估计问题。我们考虑了一个非平稳RCA过程，并证明了新息方差参数不能用拟极大似然方法估计。证明了剩余模型参数的拟极大似然估计的渐近正态性，从而证明了随机系数自回归模型不存在单位根问题。

Quasi-maximum likelihood estimation for cointegrated continuous-time state space models observed at low frequencies

In this paper, we investigate quasi-maximum likelihood (QML) estimation for the parameters of a cointegrated solution of a continuous-time linear state space model observed at discrete time points. The class of cointegrated solutions of continuous-time linear state space models is equivalent to the class of cointegrated continuous-time ARMA (MCARMA) processes. As a start, some pseudo-innovations are constructed to be able to define a QML-function. Moreover, the parameter vector is divided appropriately in long-run and short-run parameters using a representation for cointegrated solutions of co…

一类广义双曲连续时间积分随机波动率Likewise模型

A Class of Generalized Hyperbolic Continuous Time Integrated Stochastic Volatility Likelihood Models

本文讨论和分析了一类基于两种分布创新的股票收益金融模型的似然模型。也就是说，对数股票价格的总收益的边缘分布可以用广义双曲线分布很好地近似，并且可以通过将综合波动率指定为随机过程来处理波动率聚类，例如Barndorff-Nielsen和Shephard（BNS）最近的一系列论文中提出的。BNS模型产生的可能性总回报，可以被视为潜回归模型的一个子类，其中有n个条件独立的正态随机变量，其均值和方差可表示为一个共同的未观察到的泊松随机测度的线性泛函。James（2005 b）最近获得了对这种模型的精确分析，得到了用非常容易处理的傅里叶-余弦积分表示的似然表达式。在这里，我们的想法是分析一类可能性，这可以用于类似的目的，但潜在的回归模型是基于n个条件独立的模型，分布属于广义双曲分布的一个子类，其相应的参数表示为一个共同的未观察到的泊松随机测度的线性泛函。我们的模型可能与Brandorff-Nielsen（1997）和Jensen and Lunde（2001）的正态逆高斯/GARCH/A-PARCH模型最密切相关，在我们的例子中，GARCH分量被INT-GARCH过程等量所取代。可以看出，重要的是，这种可能性模型在结构上表现出完全不同的功能。该模型的一个很好的特点是，它允许在外部回归参数的建模方面更灵活。

Change point detection in autoregressive models with no moment assumptions

In this paper we consider the problem of detecting a change in the parameters of an autoregressive process, where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is proposed and its asymptotic properties are studied. In contrast to other work on change point tests using empirical likelihood, we do not assume knowledge of the location of the change point. In particular, we prove that the maximizer of the empirical likelihood is a consistent estimator for the parameters of the autoregressive model in the case …

具有缺失不定常协变量的Cox模型的渐近理论

Asymptotic theory for the Cox model with missing time-dependent covariate

通常通过Cox模型评价不定常协变量与生存时间之间的关系。不定常协变量通常作为研究过程中定期收集的纵向数据提供。然而，一个常见的问题是缺少协变量数据的发生。在这种情况下，最近的Cox模型估计方法联合建模生存和纵向协变量。然而，这种方法的理论依据仍然缺乏。本文证明了联合模型中极大似然估计的存在性和相合性。估计量的渐近分布以及渐近方差的一致估计。

The Focused Information Criterion for Stochastic Model Selection Problems Using $M$-Estimators

Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed. Towards the immediate extensions and generalizations of these results, the present article is aimed at providing the focused model selection and model averaging methods using general maximum likelihood type estimators, popularly known as $M$-estimators. The necessary asymptotic theory is derived in a setup of stationary and strong mixing stochastic processes e…

无矩条件下的非对称GARCH建模

Asymmetric GARCH modelling without moment conditions

针对厚尾和稳定性问题，提出标准化非高斯稳定创新的非对称GARCH模型，建立平稳和爆炸情形下的推理框架，证明MLE的强相合性和渐近正态性。

带有学习距离度量的Mallows模型：采样与极大似然估计

Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation

针对Mallows模型固定距离度量的局限，提出从数据中学习L_α距离度量的泛化模型，开发了FPTAS采样算法和联合极大似然估计算法，并证明了强一致性且经实证验证。

Robust Power System Dynamic State Estimator with Non-Gaussian Measurement Noise: Part I--Theory

This paper develops the theoretical framework and the equations of a new robust Generalized Maximum-likelihood-type Unscented Kalman Filter (GM-UKF) that is able to suppress observation and innovation outliers while filtering out non-Gaussian measurement noise. Because the errors of the real and reactive power measurements calculated using Phasor Measurement Units (PMUs) follow long-tailed probability distributions, the conventional UKF provides strongly biased state estimates since it relies on the weighted least squares estimator. By contrast, the state estimates and residuals of our GM-UKF …

通过CARE升级生存模型

Upgrading survival models with CARE

CARE方法通过凸组合提升生存模型的预测性能，结合新数据与外部估计器，实现更优的收敛速度和实证效果。