Related papers: Frequency Domain Statistical Inference for High-Di…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop…
A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…
Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…
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…
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…
Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
Studying the flow of information between different areas of the brain can be performed by using the so-called Partial Directed Coherence. This measure is usually evaluated by first identifying a multivariate autoregressive model, and then…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…