Convergence of covariance and spectral density estimates for high-dimensional locally stationary processes

DOI10.1214/20-AOS1954zbMath1461.62165MaRDI QIDQ2656594

Danna Zhang, Wei-Biao Wu

Publication date: 11 March 2021

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aos/1611889225

zbMATH Keywords

convergence ratelocally stationary processeshigh-dimensional time seriessecond-order statisticsHanson-Wright-type inequalities

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Inference from stochastic processes and spectral analysis (62M15) General second-order stochastic processes (60G12)

Related Items

Inferential theory for generalized dynamic factor models, An Algebraic Estimator for Large Spectral Density Matrices, Graphical models for nonstationary time series, Inverse covariance operators of multivariate nonstationary time series

Uses Software

• FinTS

Cites Work

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• Granger causality and path diagrams for multivariate time series
• Analyzing complex functional brain networks: fusing statistics and network science to understand the brain
• Graphical modelling of multivariate time series
• Covariance matrix estimation for stationary time series
• On the maximum of covariance estimators
• Empirical spectral processes for locally stationary time series
• A general science-based framework for dynamical spatio-temporal models
• Mixing properties of ARCH and time-varying ARCH processes
• Large deviations for quadratic forms of locally stationary processes
• Efficient estimation of a multivariate multiplicative volatility model
• Nonparametric regression for locally stationary time series
• Hanson-Wright inequality and sub-Gaussian concentration
• On recursive estimation for time varying autoregressive processes
• Local linear quantile estimation for nonstationary time series
• Bayesian analysis of stochastic volatility models with fat-tails and correlated errors
• Nonparametric inference of quantile curves for nonstationary time series
• Covariance regularization by thresholding
• Autocorrelation, autoregression and autoregressive approximation
• Time series: theory and methods.
• Multivariate density estimation with general flat-top kernels of infinite order
• Subsampling
• Fitting time series models to nonstationary processes
• Large deviations for quadratic functionals of Gaussian processes
• Resampling methods for dependent data
• Gaussian approximation for high dimensional time series
• Towards a general theory for nonlinear locally stationary processes
• Adaptive covariance estimation of locally stationary processes
• The uniform convergence of autocovariances
• A likelihood approximation for locally stationary processes
• Bootstraps for time series
• Partial correlation analysis for the identification of synaptic connections
• Partial directed coherence: a new concept in neural structure determination
• Large deviations for quadratic forms of stationary Gaussian processes
• A bound on tail probabilities for quadratic forms in independent random variables whose distributions are not necessarily symmetric
• Spectral analysis of high-dimensional time series
• Moderate deviations for quadratic forms in Gaussian stationary processes
• Simultaneous analysis of Lasso and Dantzig selector
• Covariance and precision matrix estimation for high-dimensional time series
• A recursive online algorithm for the estimation of time-varying ARCH parameters
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Statistical inference for time-varying ARCH processes
• CROSS-SPECTRAL ANALYSIS OF TREMOR TIME SERIES
• Nonlinear spectral density estimation: thresholding the correlogram
• Confidence estimation of the covariance function of stationary and locally stationary processes
• A Constrainedℓ₁Minimization Approach to Sparse Precision Matrix Estimation
• Estimating linear dependence between nonstationary time series using the locally stationary wavelet model
• A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
• BIAS-CORRECTED NONPARAMETRIC SPECTRAL ESTIMATION
• Automatic Statistical Analysis of Bivariate Nonstationary Time Series
• Decomposability and selection of graphical models for multivariate time series
• Time-Dependent Spectral Analysis of Nonstationary Time Series
• To batch or not to batch?
• Evolutionary Coherence of Nonstationary Signals
• Estimating Time-Evolving Partial Coherence Between Signals via Multivariate Locally Stationary Wavelet Processes
• Limit theorems for iterated random functions
• HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES
• Learning Graphical Models for Stationary Time Series
• Nonlinear system theory: Another look at dependence
• A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables
• Information Theory and Stochastics for Multiscale Nonlinear Systems
• Analysis of Financial Time Series
• SLEX Analysis of Multivariate Nonstationary Time Series
• The Generalized Dynamic Factor Model
• Graphical interaction models for multivariate time series.