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因果变化点的检测与定位AI 解读

Detecting and localizing change points in sequential data is of interest in many areas of application. Various notions of change points have been proposed, such as changes in mean, variance, or the linear regression coefficient. In this work, we consider settings in which a response variable $Y$ and a set of covariates $X=(X^1,\ldots,X^{d+1})$ are observed over time and aim to find changes in the causal mechanism generating $Y$ from $X$. More specifically, we assume $Y$ depen…

变量组因果发现的理论基础AI 解读

Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or…

密集纵向计数数据的贝叶斯多层泊松对数正态隐马尔可夫模型AI 解读

Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical environment to optimally exploit the information present in multivariate time series, uncovering the latent dynamics that rule them. Here, we extend the Poisson HMM to the multilevel framework, accommodating variability between individuals…

面向高维数据的高效张量回归AI 解读

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it…

利用非抽取小波包特征与 Transformer 模型进行时间序列预测AI 解读

This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of vanishing moments as input features to both non-temporal and temporal forecasting methods, by selecting these numbers during the cross-validation phase. Secondly, we compare the use of both the non-decimated wavelet transform and the…

高维向量误差修正模型的贝叶斯分析AI 解读

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated…

带加性噪声的周期自回归模型：估计与检验的实证研究AI 解读

Periodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be disturbed by additional noise related to measurement device disturbances or to other external sources. Thus, the known estimation techniques dedicated for PAR models may be inefficient for such cases. When the variance of the additive noise…

样本分割与时间序列拟合优度评估AI 解读

A fundamental and often final step in time series modeling is to assess the quality of fit of a proposed model to the data. Since the underlying distribution of the innovations that generate a model is often not prescribed, goodness-of-fit tests typically take the form of testing the fitted residuals for serial independence. However, these fitted residuals are inherently dependent since they are based on the same parameter estimates and thus standard tests of serial…

利用可变带通周期块自助法研究美国新冠死亡的季节与周期模式AI 解读

Since the emergence of the SARS-CoV-2 virus, research into the existence, extent, and pattern of seasonality has been of the highest importance for public health preparation. This study uses a novel bandpass bootstrap approach called the Variable Bandpass Periodic Block Bootstrap (VBPBB) to investigate the periodically correlated (PC) components including seasonality within US COVID-19 mortality. Bootstrapping to produce confidence intervals (CI) for periodic characteristics…

分组时变网络向量自回归模型的估计AI 解读

This paper introduces a flexible time-varying network vector autoregressive model framework for large-scale time series. A latent group structure is imposed on the heterogeneous and node-specific time-varying momentum and network spillover effects so that the number of unknown time-varying coefficients to be estimated can be reduced considerably. A classic agglomerative clustering algorithm with nonparametrically estimated distance matrix is combined with a ratio criterion…

灵活的全局预测组合AI 解读

Forecast combination -- the aggregation of individual forecasts from multiple experts or models -- is a proven approach to economic forecasting. To date, research on economic forecasting has concentrated on local combination methods, which handle separate but related forecasting tasks in isolation. Yet, it has been known for over two decades in the machine learning community that global methods, which exploit task-relatedness, can improve on local methods that ignore it.…

使用稀疏性排序 Lasso 进行快速、有效且一致的时间序列建模AI 解读

The sparsity-ranked lasso (SRL) has been developed for model selection and estimation in the presence of interactions and polynomials. The main tenet of the SRL is that an algorithm should be more skeptical of higher-order polynomials and interactions *a priori* compared to main effects, and hence the inclusion of these more complex terms should require a higher level of evidence. In time series, the same idea of ranked prior skepticism can be applied to the possibly…

指数平滑的新理论框架AI 解读

Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb procedure. We introduce a novel theoretical perspective where the recursive equation that defines simple exponential smoothing occurs naturally as a stochastic gradient ascent scheme to optimize a sequence of Gaussian log-likelihood functions.…

数据驱动的两阶段多划分时间序列因果集成模型AI 解读

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to identify linear relationships, while others are applicable for non-linearities. Algorithms further vary in their sensitivity to noise and their ability to infer causal information from coupled vs. non-coupled time series. Therefore,…

基于小波的周期性自回归移动平均模型AI 解读

This paper proposes a wavelet-based method for analysing periodic autoregressive moving average (PARMA) time series. Even though Fourier analysis provides an effective method for analysing periodic time series, it requires the estimation of a large number of Fourier parameters when the PARMA parameters do not vary smoothly. The wavelet-based analysis helps us to obtain a parsimonious model with a reduced number of parameters. We have illustrated this with simulated and…

计数时间序列的 Tobit 模型AI 解读

Several models for count time series have been developed during the last decades, often inspired by traditional autoregressive moving average (ARMA) models for real-valued time series, including integer-valued ARMA (INARMA) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. Both INARMA and INGARCH models exhibit an ARMA-like autocorrelation function (ACF). To achieve negative ACF values within the class of INGARCH models, log and…

分位数相干性的半参数估计及双变量金融时间序列聚类应用AI 解读

In multivariate time series analysis, spectral coherence measures the linear dependency between two time series at different frequencies. However, real data applications often exhibit nonlinear dependency in the frequency domain. Conventional coherence analysis fails to capture such dependency. The quantile coherence, on the other hand, characterizes nonlinear dependency by defining the coherence at a set of quantile levels based on trigonometric quantile regression. This…

时间序列非参数回归中基于差分的协方差矩阵估计及其设定检验应用AI 解读

Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt structural breaks and its competitive finite sample performance. However, existing methods mainly focus on estimators for the univariate process while their direct and multivariate extensions for most linear models are asymptotically…

高维非高斯数据的组合分位数预测AI 解读

This study proposes a novel method for forecasting a scalar variable based on high-dimensional predictors that is applicable to various data distributions. In the literature, one of the popular approaches for forecasting with many predictors is to use factor models. However, these traditional methods are ineffective when the data exhibit non-Gaussian characteristics such as skewness or heavy tails. In this study, we newly utilize a quantile factor model to extract quantile…

时间序列的在线自助法AI 解读

Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series or spatially correlated observations. In this paper, we propose a novel bootstrap method that is designed to account for data dependencies and can be executed online, making it particularly suitable for real-time applications. This method…

基于模拟的转移密度近似与随机微分方程模型推断AI 解读

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given problem, certain model parameters remain unknown. Efficiently inferring these unknown parameters based on observations of the state in discrete time series represents a vital practical subject. The challenge arises in nonlinear SDEs, where…

基于变分自编码器的多层神经格兰杰因果连接学习框架AI 解读

Granger causality has been widely used in various application domains to capture lead-lag relationships amongst the components of complex dynamical systems, and the focus in extant literature has been on a single dynamical system. In certain applications in macroeconomics and neuroscience, one has access to data from a collection of related such systems, wherein the modeling task of interest is to extract the shared common structure that is embedded across them, as well as…

用于高维时间序列的可解释且高效的无限阶向量自回归模型AI 解读

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and difficulty of interpretation, especially for high-dimensional time series. This paper proposes a novel sparse infinite-order VAR model for high-dimensional time…

基于保均值随机舍入的整数值 ARMA 模型AI 解读

In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the use of the rounding operator is very natural. Because of the discontinuity of the rounding operator, the formulation of the corresponding model identifiability conditions and the computation of parameter estimators need special attention.…