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Time Series Analysis of Rankings: A GARCH-Type Approach

排名时间序列分析:一种 GARCH 型方法

Ranking data are frequently obtained nowadays but there are still scarce methods for treating these data when temporally observed. The present paper contributes to this topic by proposing and developing novel models for handling time series of ranking data. We introduce a class of time-varying ranking models inspired by the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models. More specifically, the temporal dynamics are defined by the conditional…

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A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks

高斯平滑转换向量自回归模型及严重天气冲击的宏观效应

We introduce a new smooth transition vector autoregressive model with a Gaussian conditional distribution and transition weights that, for a $p$th order model, depend on the full distribution of the preceding $p$ observations. Specifically, the transition weight of each regime increases in its relative weighted likelihood. This data-driven approach facilitates capturing complex switching dynamics, enhancing the identification of gradual regime shifts. In an empirical…

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Forecasting density-valued functional panel data

密度值函数型面板数据的预测

We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We implement a center log-ratio transformation to transform densities into unconstrained functions. These functions exhibit cross-sectional correlation and temporal dependence. Via a functional analysis of variance decomposition, we decompose…

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Ordinal Patterns Based Change Points Detection

基于序模式的变点检测

The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of the time series. In this work, we prove the asymptotic normality of the relative frequency of ordinal patterns for time series with linear increments. Moreover, we apply ordinal patterns to detect changes in the distribution of a time…

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Online Generalized Method of Moments for Time Series

时间序列的在线广义矩估计

Online learning has gained popularity in recent years due to the urgent need to analyse large-scale streaming data, which can be collected in perpetuity and serially dependent. This motivates us to develop the online generalized method of moments (OGMM), an explicitly updated estimation and inference framework in the time series setting. The OGMM inherits many properties of offline GMM, such as its broad applicability to many problems in econometrics and statistics, natural…

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Dynamic treatment effects: high-dimensional inference under model misspecification

动态处理效应:模型误设下的高维推断

Estimating dynamic treatment effects is crucial across various disciplines, providing insights into the time-dependent causal impact of interventions. However, this estimation poses challenges due to time-varying confounding, leading to potentially biased estimates. Furthermore, accurately specifying the growing number of treatment assignments and outcome models with multiple exposures appears increasingly challenging to accomplish. Double robustness, which permits model…

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An Adaptive Moving Average for Macroeconomic Monitoring

用于宏观经济监测的自适应移动平均

The use of moving averages is pervasive in macroeconomic monitoring, particularly for tracking noisy series such as inflation. The choice of the look-back window is crucial. Too long of a moving average is not timely enough when faced with rapidly evolving economic conditions. Too narrow averages are noisy, limiting signal extraction capabilities. As is well known, this is a bias-variance trade-off. However, it is a time-varying one: the optimal size of the look-back window…

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The Dynamic Triple Gamma Prior as a Shrinkage Process Prior for Time-Varying Parameter Models

时变参数模型的动态三重伽马收缩过程先验

Many existing shrinkage approaches for time-varying parameter (TVP) models assume constant innovation variances across time points, inducing sparsity by shrinking these variances toward zero. However, this assumption falls short when states exhibit large jumps or structural changes, as often seen in empirical time series analysis. To address this, we propose the dynamic triple gamma prior -- a stochastic process that induces time-dependent shrinkage by modeling dependence…

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Testing and Estimating Structural Breaks in Time Series and Panel Data in Stata

在 Stata 中检验和估计时间序列与面板数据的结构突变

Identifying structural change is a crucial step in analysis of time series and panel data. The longer the time span, the higher the likelihood that the model parameters have changed as a result of major disruptive events, such as the 2007--2008 financial crisis and the 2020 COVID--19 outbreak. Detecting the existence of breaks, and dating them is therefore necessary, not only for estimation purposes but also for understanding drivers of change and their effect on…

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Irregular measurement times in estimating time-varying treatment effects: Categorizing biases and comparing adjustment methods

时变处理效应估计中的不规则测量时点:偏差分类与调整方法比较

To estimate the causal effect of treatments that vary over time from observational data, one must adjust for time-varying confounding. A common procedure to address confounding is the use of inverse probability of treatment weighting methods. However, the timing of covariate measurements is often irregular, which may introduce additional confounding bias as well as selection bias into the causal effect estimate. Two reweighting methods have been proposed to adjust for these…

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A Robust Residual-Based Test for Structural Changes in Factor Models

因子模型结构变化的稳健残差检验

In this paper, we propose an easy-to-implement residual-based specification testing procedure for detecting structural changes in factor models, which is powerful against both smooth and abrupt structural changes with unknown break dates. The proposed test is robust against the over-specified number of factors, and serially and crosssectionally correlated error processes. A new central limit theorem is given for the quadratic forms of panel data with dependence over both…

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Penalized G-estimation for effect modifier selection in a structural nested mean model for repeated outcomes

重复结果结构嵌套均值模型中效应修饰变量选择的惩罚 G 估计

Effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. Modeling these effect differences is important for etiological goals and for purposes of optimizing treatment. Structural nested mean models (SNMMs) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. A…

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Recovering latent linkage structures and spillover effects with structural breaks in panel data models

面板模型结构突变下潜在联系结构与溢出效应的恢复

This paper introduces a framework to analyze time-varying spillover effects in panel data. We consider panel models where a unit's outcome depends not only on its own characteristics (private effects) but also on the characteristics of other units (spillover effects). The linkage of units is allowed to be latent and may shift at an unknown breakpoint. We propose a novel procedure to estimate the breakpoint, linkage structure, spillover and private effects. We address the…

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Change-point Detection and Segmentation of Discrete Data using Bayesian Context Trees

利用贝叶斯上下文树检测离散数据变点并进行分段

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building on the recently introduced Bayesian Context Trees (BCT) framework, the distributions of different segments in a discrete time series are described as variable-memory Markov chains. Inference for the presence and location of change-points…

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Choosing the Right Norm for Change Point Detection in Functional Data

函数型数据变点检测中的范数选择

We consider the problem of detecting a change point in a sequence of mean functions from a functional time series. We propose an $L^1$ norm based methodology and establish its theoretical validity both for classical and for relevant hypotheses. We compare the proposed method with currently available methodology that is based on the $L^2$ and supremum norms. Additionally we investigate the asymptotic behaviour under the alternative for all three methods and showcase both…

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Gradual changes in functional time series

函数型时间序列中的渐进变化

We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between a benchmark function and the mean functions at different time points. We speak of a gradual change of size $Δ$, if this quantity exceeds a given threshold $Δ>0$. For example, the benchmark function could represent an average of yearly…

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Modelling Loss of Complexity in Intermittent Time Series and its Application

间歇性时间序列的复杂性损失建模及其应用

In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each intermittent time series, where the corresponding lag order and the loss of complexity are determined by Bayesian Information Criterion (BIC) and relative entropy respectively. Then, change-points in the complexity are detected by a cumulative…

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Copula Central Asymmetry of Equity Portfolios

股票投资组合的 Copula 中心不对称性

Financial crises are usually associated with increased cross-sectional dependence between asset returns, causing asymmetry between the lower and upper tail of return distribution. The detection of asymmetric dependence is now understood to be essential for market supervision, risk management, and portfolio allocation. I propose a non-parametric test procedure for the hypothesis of copula central symmetry based on the Cramér-von Mises distance of the empirical copula and its…

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From sparse to dense functional time series: phase transitions of detecting structural breaks and beyond

从稀疏到稠密的函数型时间序列:结构突变检测的相变及拓展

We develop a novel methodology for detecting abrupt break points in mean functions of functional time series, adaptable to arbitrary sampling schemes. By employing B-spline smoothing, we introduce $\mathcal L_{\infty}$ and $\mathcal L_2$ test statistics statistics based on a smoothed cumulative summation (CUMSUM) process, and derive the corresponding asymptotic distributions under the null and local alternative hypothesis, as well as the phase transition boundary from sparse…

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GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Imaging Studies

GLACIAL:面向纵向影像研究的格兰杰与学习式因果分析

The Granger framework is useful for discovering causal relations in time-varying signals. However, most Granger causality (GC) methods are developed for densely sampled timeseries data. A substantially different setting, particularly common in medical imaging, is the longitudinal study design, where multiple subjects are followed and sparsely observed over time. Longitudinal studies commonly track several biomarkers, which are likely governed by nonlinear dynamics that might…

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Multiscale Autoregression on Adaptively Detected Timescales

基于自适应检测时间尺度的多尺度自回归

We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent averages of the process over multiple timescales, whose number or spans are not known to the analyst and are estimated from the data via a change-point detection technique. The resulting construction, termed Adaptive Multiscale AutoRegression…

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Forecasting realized covariances using HAR-type models

使用HAR类模型预测已实现协方差矩阵

We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First,…

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Sequential Change Point Detection in High-dimensional Vector Auto-regressive Models

高维向量自回归模型中的序贯变点检测

Sequential (online) change-point detection involves continuously monitoring time-series data and triggering an alarm when shifts in the data distribution are detected. We propose an algorithm for real-time identification of alterations in the transition matrices of high-dimensional vector autoregressive models. The algorithm estimates transition matrices and error term variances using regularization techniques applied to training data, then computes a specific test statistic…

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Emperical Study on Various Symmetric Distributions for Modeling Time Series

多种对称分布用于时间序列建模的实证比较

This study evaluated probability distributions for modeling time series with abrupt structural changes. The Pearson type VII distribution, with an adjustable shape parameter $b$, proved versatile. The generalized Laplace distribution performed similarly to the Pearson model, occasionally surpassing it in terms of likelihood and AIC. Mixture models, including the mixture of $δ$-function and Gaussian distribution, showed potential but were less stable. Pearson type VII and…

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