论文检索

利用中心对称核进行谱密度估计中的短滞后差分AI 解读

Summary Mean-robust estimation of spectral density and long-run variance is crucial for many statistical inference procedures. However, existing methods often degrade when serially dependent data exhibit volatile, time-varying trends, or sudden jumps, particularly in small samples. While differencing and kernel averaging are standard tools for achieving mean robustness and consistency, they are not inherently compatible. Combining them can compromise optimality.…

积分概率度量引导的 CUSUM-Net 非参数变点检测AI 解读

Abstract We propose CUSUM-Net, a nonparametric method for changepoint detection based on integral probability metrics and deep neural networks. Our approach learns a critic function by maximizing an aggregate CUSUM objective over candidate changepoints, thereby linking changepoint detection to optimization of two-sample integral probability metrics. The learned critic induces a one-dimensional representation on which changepoints are localized by a classical CUSUM scan.…

高维向量与张量时间序列的重尾稳健因子建模AI 解读

Summary We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with nonnegligible probability. We propose combining a two-step procedure for tensor decomposition with data truncation, which is easy to implement and does not require an iterative search for a numerical solution. Departing from the light-tail assumptions often adopted in the time series factor-modelling…

高维主成分分析中显著成分数量的估计AI 解读

Abstract We consider the problem of estimating the number of significant components in high-dimensional principal component analysis. We propose a new penalized approach using the explained variance ratio and the rigidity of the nonspiked sample eigenvalues of sample covariance matrices of $ p $ variables. Compared with methods in the existing literature, the consistency of the proposed estimator holds, not only for independent data, but also for some times series data when…

张量因子模型中Kronecker积结构的检验AI 解读

Abstract We propose a test for the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. By defining a Kronecker product structure set, we determine whether a tensor time series has a Kronecker product structure, equivalent to its ability to decompose the series according to a tensor factor model. Our test is built on analysing and comparing the residuals from fitting a full tensor factor…

二次谱估计量的偏误修正AI 解读

Summary The three cardinal, statistically consistent families of nonparametric estimators for the power spectral density of a time series are the lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample, each can be subject to nonignorable bias. Astfalck et al. (2024) developed a method that offers significant bias reduction for finite samples for Welch’s estimator, which this article extends to the larger family of…

高维重复事件的动态因子分析AI 解读

Summary Recurrent event time data arise in many studies, including in biomedicine, public health, marketing and social media analysis. High-dimensional recurrent event data involving many event types and observations have become prevalent with advances in information technology. This article proposes a semiparametric dynamic factor model for the dimension reduction of high-dimensional recurrent event data. The proposed model imposes a low-dimensional structure on the mean…

利用联合特征函数对多元时间序列进行非参数分段AI 解读

Summary Modern time series data often exhibit complex dependence and structural changes that are not easily characterized by shifts in the mean or model parameters. We propose a nonparametric data segmentation methodology for multivariate time series. By considering joint characteristic functions between the time series and its lagged values, our proposed method is able to detect changepoints in the marginal distribution, but also those in possibly nonlinear serial…

连续时间局部平稳小波过程AI 解读

Abstract This article introduces the class of continuous-time locally stationary wavelet processes. Continuous-time models enable us to properly provide scale-based time series models for irregularly spaced observations for the first time, while also permitting a spectral representation of the process over a continuous range of scales. We derive results for both the theoretical setting, where we assume access to the entire process sample path, and a more practical one, which…

样本分割与时间序列拟合优度评估AI 解读

Summary A fundamental and often final step in time series modelling 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 intrinsically dependent since they are based on the same parameter estimates, and thus standard tests of…

局部平稳时间序列的偏自相关函数：刻画、估计与推断AI 解读

SUMMARY For stationary time series, it is common to use plots of the partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of the process. To the best of our knowledge, analogues for nonstationary time series have not yet been fully developed. This article aims to fill this gap for locally stationary time series with short-range dependence. First, we characterize the PACF locally in the time domain and show that the jth PACF…

跳跃抽样：频域中的子抽样AI 解读

Summary Over the last 35 years, several bootstrap methods for time series have been proposed. Popular time domain methods include the block bootstrap, the stationary bootstrap, the linear process bootstrap, among others; subsampling for time series is also available, and is closely related to the block bootstrap. The frequency domain bootstrap has been performed either by resampling the periodogram ordinates or by resampling the ordinates of the discrete Fourier transform.…

Welch 谱密度估计方法的去偏AI 解读

Abstract Welch’s method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite-length time series, while the variance of the estimator decreases as the number of segments increases, the magnitude of the estimator’s bias increases: a bias-variance trade-off ensues when setting the segment number. We address this issue by providing…

存在漏报时的时间序列序列依赖与交叉依赖检验AI 解读

Abstract In practice, it is common for collected data to be underreported, an issue that is particularly prevalent in fields such as the social sciences, ecology and epidemiology. Drawing inferences from such data using conventional statistical methods can lead to incorrect conclusions. In this paper, we study tests for serial or cross dependence in time series data that are subject to underreporting. We introduce new test statistics, develop corresponding group-of-blocks…

面向多分辨率数据的个体化动态潜因子模型及其移动健康应用AI 解读

Summary Mobile health has emerged as a major success for tracking individual health status, due to the popularity and power of smartphones and wearable devices. This has also brought great challenges in handling heterogeneous, multi-resolution data that arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model for irregular multi-resolution time series…

时间序列非参数回归中的差分协方差矩阵估计及其设定检验应用AI 解读

Summary 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…

多变量高斯时间序列偏相关系数的推断AI 解读

Abstract We derive an asymptotic joint distribution and novel covariance estimator for the partial correlations of a multivariate Gaussian time series under mild regularity conditions. Using our derived asymptotic distribution, we develop a Wald confidence interval and testing procedure for inference of individual partial correlations for time series data. Through simulation we demonstrate that our proposed confidence interval attains higher coverage rates and our testing…

时间平均方差常数的渐近恒定风险估计量AI 解读

Summary Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top…

Toeplitz 协方差矩阵的高效非参数估计AI 解读

Abstract A new efficient nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal…

对象值时间序列的序列独立性检验AI 解读

Summary We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a…

得分驱动模型的最优性AI 解读

Summary Score-driven models have recently been introduced as a general framework to specify time-varying parameters of conditional densities. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback–Leibler divergence between the true conditional…

Page 之后七十年：累积和序贯变点检验的发展现状AI 解读

Abstract Quality control charts aim at raising an alarm as soon as sequentially obtained observations of an underlying random process no longer seem to be within stochastic fluctuations prescribed by an in-control scenario. Such random processes can often be modelled using the concept of stationarity, or even independence as in most classical works. An important out-of-control scenario is the changepoint alternative, for which the distribution of the process changes at an…

时间序列预测误差的估计AI 解读

Summary The accurate estimation of prediction errors in time series is an important problem, which has immediate implications for the accuracy of prediction intervals as well as the quality of a number of widely used time series model selection criteria such as the Akaike information criterion. Except for simple cases, however, it is difficult or even impossible to obtain exact analytical expressions for one-step and multi-step predictions. This may be one of the reasons…

矩阵值函数平滑特征向量的√2估计AI 解读

Summary Modern statistical methods for multivariate time series rely on the eigendecomposition of matrix-valued functions such as time-varying covariance and spectral density matrices. The curse of indeterminacy or misidentification of smooth eigenvector functions has not received much attention. We resolve this important problem and recover smooth trajectories by examining the distance between the eigenvectors of the same matrix-valued function evaluated at two consecutive…