Covariance and precision matrix estimation for high-dimensional time series

By Xiaohui Chen, Mengyu Xu, Wei Biao Wu. 2013

152 citations recorded by the source corpus.

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate of convergence. Asymptotic properties are also obtained for the precision matrix estimate which is based on the graphical Lasso principle. Our theory substantially generalizes earlier ones by allowing dependence, by allowing nonstationarity and by relaxing the associated moment conditions.

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6250ec6e71637d3f3e7a32c83a7d2c1d3dc4c534

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Xiaohui Chen
2. Tommaso Cai
3. Danna Zhang
4. Mengjia Yu
5. Harrison H. Zhou
6. Wei Biao Wu
7. Moritz Jirak
8. Zhao Ren

In Finance

1. Xiaohui Chen
2. Danna Zhang
3. Moritz Jirak
4. Tommaso Cai
5. Zhao Ren
6. Harrison H. Zhou
7. Mengjia Yu
8. Wei Biao Wu

In Statistics and Probability

1. Tommaso Cai
2. Zhao Ren
3. Harrison H. Zhou
4. Xiaohui Chen
5. Mengjia Yu
6. Wei Biao Wu
7. Danna Zhang
8. Moritz Jirak

Citations in the corpus

• Estimation and Selection of Spatial Weight Matrix in a Spatial Lag Model (2019, unknown): “See Chen, Xu, and Wu (2013).”
• Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications (2016, methodology): “High probability bounds of τ were given in [10, 20] and asymptotic”
• Gaussian Approximation for High Dimensional Time Series (2015, background): “Chen et al. (2013) and Zhang and Cheng (2014) considered some special cases: the former paper requires that max 1 ≤ j ≤ p X · j q,α ≤ C while the latter imposes the stronger geometric moment contraction condition max 1 ≤ j ≤ p ∆ m,q,j ≤ Cρ m with ρ ∈ (0 , 1), and in both cases the constant C does…”
• Uniform change point tests in high dimension (2015, background): “Another advantage is that these dependence measures have a natural spatial extension which includes the univariate (multivariate) case as a special example; see, for instance, [14, 42].”
• Finite sample change point inference and identification for high‐dimensional mean vectors (2017, background): “If p is larger (or even much larger) than n, then estimation of Σ itself becomes a challenging problem and the spectral norm consistency of Σ (or the inverse Σ−1) is possible under additional structural assumptions (such as sparsity) on the covariance matrix [8, 9, 11, 12, 15].”
• Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “Recently, Chen et al. (2013) and Basu and Michailidis (2015) considered sparse covariance matrix estimation for time series data based on certain dependence measures, which play an important role in the rates of convergence.”