Sparse High-Dimensional Vector Autoregressive Bootstrap
稀疏高维向量自回归自助法AI 解读 ↓
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稀疏高维向量自回归自助法AI 解读 ↓
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We introduce a high-dimensional multiplier bootstrap for time series data based on capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of independent interest.
通过条件中心化进行非线性 Granger 因果的 RKHS 推断
Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a reproducing kernel Hilbert space (RKHS)-based test for nonlinear Granger non-causality in conditional mean for nonlinear autoregressive processes. The key idea is a conditional-centering decomposition of the target regression function into an own-history component and an orthogonal component…
高维二元时间序列的统计推断
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.…
通过重抽样与模型聚合稀疏估计广义向量自回归的参数支撑集
The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series. We develop an algorithm that performs the estimation by aggregating support sets obtained by applying the LASSO to data subsamples. Our approach is to identify several candidate models and estimate S by selecting common parameters, thus…
大型向量自回归模型中的网络格兰杰因果关系发现
This article proposes novel inferential procedures for discovering the network Granger causality in highdimensional vector autoregressive models.In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR).The first procedure is based on the limiting normal distribution of the t-statistics with the debiased lasso estimator.The second procedure is its bootstrap version.We also provide a robustification of the first…
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
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…
特异成分服从稀疏 VAR 的因子模型
We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector autoregressive model (VAR) {which allows} for cross-sectional and time dependence. The estimation is articulated in two steps: first, the factors and their loadings are estimated via principal component analysis and second, the sparse VAR is…