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平稳函数时间序列的模型设定检验AI 解读

We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample size. Different model assumptions induce different structural restrictions on these kernels, and our tests are constructed by measuring deviations from the…

非平稳时间序列的递归多变点检测、估计与置信区间AI 解读

We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous calibration of the critical values at each stage of the recursion, BARBS ensures control of the Type I error under the null hypothesis of no…

基于自希尔伯特–施密特独立性准则的序列独立性检验AI 解读

We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between an observation and its lagged counterpart, providing a kernel-based approach to detecting nonlinear serial dependence. The empirical AutoHSIC statistic is a lagged U-statistic constructed from overlapping observations, and hence inherits…

非线性时间序列的同时推断：筛法 M 回归方法AI 解读

This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the development of uncertainty quantification over the entire predictor space unexplored. We address this gap by establishing a uniform Bahadur representation for the sieve M-estimator, accommodating dependent data and a growing number of sieve…

时间序列函数型线性回归的同时推断AI 解读

We consider the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization approach with flexible choices of orthonormal basis functions. A simple and unified multiplier bootstrap methodology is proposed for the JSCB construction which is shown to achieve the correct coverage probability asymptotically. Furthermore,…

高维分段局部平稳时间序列的复杂趋势推断AI 解读

This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting latent group structures to estimate trend functions. In the first step, we propose AJDN (Asynchronous Jump Detection under Nonstationary Noise), a multiscale framework for the identification and localization of jumps in high-dimensional…

复杂非平稳噪声下同步压缩变换的不确定性量化AI 解读

We propose a bootstrapping framework to quantify uncertainty in time-frequency representations (TFRs) generated by the short-time Fourier transform (STFT) and the STFT-based synchrosqueezing transform (SST) for oscillatory signals with time-varying amplitude and frequency contaminated by complex nonstationary noise. To this end, we leverage a recent high-dimensional Gaussian approximation technique to establish a sequential Gaussian approximation for nonstationary processes…

时变非线性时间序列回归的筛估计与同时推断AI 解读

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform consistency. Second, we develop a unified simultaneous inferential theory to conduct both structural and exact form tests on these functions. Additionally, we introduce a multiplier bootstrap procedure for practical implementation. Our…

维度增长的非平稳时间序列的 Wasserstein 与凸集高斯逼近AI 解读

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference problems. To date, most GA results for high-dimensional time series are established on hyper-rectangles and their equivalence. In this paper, by considering the 2-Wasserstein distance and the collection of all convex sets, we establish a…

复杂时间动态下 M 回归的自卷积 BootstrapAI 解读

The paper considers simultaneous nonparametric inference for a wide class of M-regression models with time-varying coefficients. The covariates and errors of the regression model are tackled as a general class of nonstationary time series and are allowed to be cross-dependent. A novel and easy-to-implement self-convolved bootstrap procedure is proposed. With only one tuning parameter, the bootstrap facilitates a $\sqrt{n}$-consistent inference of the cumulative regression…

不等式约束下非平稳时间序列分位数回归的推断AI 解读

We consider parameter inference for linear quantile regression with non-stationary predictors and errors, where the regression parameters are subject to inequality constraints. We show that the constrained quantile coefficient estimators are asymptotically equivalent to the metric projections of the unconstrained estimator onto the constrained parameter space. Utilizing a geometry-invariant property of this projection operation, we propose inference procedures - the Wald,…

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

For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary time series have not been fully established yet. In this paper, we 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 $j$th PACF,…

局部平稳函数型时间序列的最优短期预测AI 解读

Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term linear prediction of non-stationary functional or curve time series with smoothly time-varying data generating mechanisms. The core of this work is to establish a unified functional auto-regressive approximation result for a general class…

非平稳时间序列的自回归逼近：推断与应用AI 解读

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent non-stationary and nonlinear time series can be well approximated globally by a white-noise-driven auto-regressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a structural approximation…

时变非线性时间序列回归的筛法同时推断AI 解读

In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which can achieve the min-max optimal rate. On the other hand, we develop a unified simultaneous inferential theory which can be used to conduct both structural and exact form testings on the functions. Our proposed statistics are powerful even…