Related papers: Bootstrapping High Dimensional Time Series
We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
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…
The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute…
We propose a bootstrap-based test to detect a mean shift in a sequence of high-dimensional observations with unknown time-varying heteroscedasticity. The proposed test builds on the U-statistic based approach in Wang et al. (2022), targets…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
This paper presents a bootstrapped p-value white noise test based on the maximum correlation, for a time series that may be weakly dependent under the null hypothesis. The time series may be prefiltered residuals. The test statistic is a…
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…
We propose robust two-sample tests for comparing means in time series. The framework accommodates a wide range of applications, including structural breaks, treatment-control comparisons, and group-averaged panel data. We first consider…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be…
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…
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…
This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…
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…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process.…
We consider the problem of inference after model selection under weak assumptions in the time series setting. Even when the data are not independent, we show that sample splitting remains asymptotically valid as long as the process…
In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…