论文检索

高维线性回归的统一谱分析：去偏与阈值化AI 解读

We use spectral analysis to establish a unified theory of debiasing, thresholding, and simultaneous inference for high-dimensional linear regression with ill-conditioned designs. The methods include Ridge regression, spectral cut-off, and iterative and dynamical regression procedures. A common debiasing procedure uses two applications of the original linear algorithm with fixed parameters. Spectral analysis shows that debiasing squares the residual, while implementations…

高维非平稳时间序列的独立性检验AI 解读

This manuscript studies the problem of independence testing between two high-dimensional time series without assuming weak stationarity, that is, allowing their autocovariances to vary over time. To this end, we propose a bimodal weighted-average test statistic that removes the bias induced by temporal dependence under the null hypothesis, thereby avoiding the need to whiten the time series prior to hypothesis testing -- a procedure that is challenging in high-dimensional…

ProbRes：面向概率时间序列预测的波动率学习AI 解读

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the…

高维二元时间序列的统计推断AI 解读

The analysis of non-real-valued data, such as binary time series, has attracted great interest in recent years. This manuscript proposes a post-selection estimator for estimating the coefficient matrices of a high-dimensional generalized binary vector autoregressive process and establishes a Gaussian approximation theorem for the proposed estimator. Furthermore, it introduces a second-order wild bootstrap algorithm to enable statistical inference on the coefficient matrices.…

高维非平稳时间序列的方差分析AI 解读

Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test statistic suitable for high-dimensional, non-stationary time series. Recognizing that the presence of complex fourth-order cumulants may introduce difficulties in variance estimation of the test statistic, we develop a bootstrap algorithm…

非独立同分布创新下高维向量自回归时间序列的统计推断AI 解读

Independent or i.i.d. innovations is an essential assumption in the literature for analyzing a vector time series. However, this assumption is either too restrictive for a real-life time series to satisfy or is hard to verify through a hypothesis test. This paper performs statistical inference on a sparse high-dimensional vector autoregressive time series, allowing its white noise innovations to be dependent, even non-stationary. To achieve this goal, it adopts a…

弱条件下时间序列二阶参数的同时统计推断AI 解读

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimation…