Comments on the presence of serial correlation in the random coefficients of an autoregressive process

自回归过程中任意阶残差相关的检验

Testing for residual correlation of any order in the autoregressive process

我们感兴趣的是在一个稳定的自回归过程中的线性自相关驱动噪声的影响，通常的最小二乘估计的渐近行为。我们表明，最小二乘估计是不一致的，我们建议一个尖锐的分析，其几乎必然的极限值以及它的渐近正态性。我们还建立了驱动噪声序列相关参数估计的几乎必然收敛性和渐近正态性。然后，我们推导出一个统计过程，使任何顺序的自回归模型的残差的相关性测试，给出明显优于常用的组合测试的Ljung-Box和Box-Pierce的结果，并出现优于小样本的Breusch-Godfrey程序。

Scale mixture of skew-normal linear mixed models with within-subject serial dependence

In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. In this paper we consider an extension of skew-normal/independent linear mixed models introduced by Lachos et al. (2010), where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM-type algorithm fo…

关于稳定自回归过程的Durbin H检验的进一步结果

Further results on the H-Test of Durbin for stable autoregressive processes

研究了当驱动噪声为一阶自回归过程时，稳定的$p-$阶自回归过程的Durbin-Watson统计量的渐近性态.它是Bercu和Proïa以前专门研究$p=1$特殊情况的工作的延伸。我们建立了自回归过程的未知向量参数的最小二乘估计以及与驱动噪声相关的序列相关估计的几乎必然收敛和渐近正态性。此外，还给出了估计的几乎必然收敛速度.然后，我们证明了几乎必然收敛和渐近正态性的Durbin-Watson统计量，我们推导出一个双边的统计过程来测试存在一个显着的一阶残差自相关，似乎澄清和改善著名的\textit{h-test}建议的Durbin。最后，我们简要总结了我们对模拟样本的观察。

一阶自回归过程Durbin-Watson统计量渐近性态的一个精确分析

A sharp analysis on the asymptotic behavior of the Durbin-Watson statistic for the first-order autoregressive process

本文的目的是对Durbin-Watson统计量的渐近性态提供一个精确的分析。我们把注意力集中在一阶自回归过程中，驱动噪声也是由一阶自回归过程。我们建立了自回归过程未知参数的最小二乘估计以及与驱动噪声相关的序列相关估计的几乎必然收敛和渐近正态性。此外，还给出了估计的几乎必然收敛速度.它允许我们建立Durbin-Watson统计量的几乎必然收敛和渐近正态性。最后，我们提出了一种新的双边统计检验残差自相关。

Moments of Maximum: Segment of AR(1)

Let $X_{t}$ denote a stationary first-order autoregressive process. Consider five contiguous observations (in time $t$) of the series (e.g., $X_{1}, ..., X_{5}$). Let $M$ denote the maximum of these. Let $ρ$ be the lag-one serial correlation, which satisfies $|ρ| < 1$. For what value of $ρ$ is $\mathbb{E}(M)$ maximized? How does $\mathbb{V}(M)$ behave for increasing $ρ$? Answers to these questions lie in Afonja (1972), suitably decoded.

Number of Sign Changes: Segment of AR(1)

Let $X_{t}$ denote a stationary first-order autoregressive process. Consider $n$ contiguous observations (in time $t$) of the series (e.g., $X_{1}, ..., X_{n}$). Let its mean be zero and its lag-one serial correlation be $ρ$, which satisfies $|ρ| < 1$. Rice (1945) proved that $(n-1) \arccos(ρ)/π$ is the expected number of sign changes. A corresponding formula for higher-order moments was proposed by Nyberg, Lizana & Ambjörnsson (2018), based on an independent interval approximation. We focus on the variance only, for small $n$, and see a promising fit between theory and model.