Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach

• URL: http://arxiv.org/abs/2012.05757v1
• Date: Thu, 10 Dec 2020 15:41:17 GMT
• Title: Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach
• Authors: Vincent W. C. Tan, Stefan Zohren
• Abstract summary: We introduce a novel covariance estimator that exploits the heteroscedastic nature of financial time series. By attenuating the noise from both the cross-sectional and time-series dimensions, we empirically demonstrate the superiority of our estimator over competing estimators.
• Score: 1.90365714903665
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel covariance estimator that exploits the heteroscedastic nature of financial time series by employing exponential weighted moving averages and shrinking the in-sample eigenvalues through cross-validation. Our estimator is model-agnostic in that we make no assumptions on the distribution of the random entries of the matrix or structure of the covariance matrix. Additionally, we show how Random Matrix Theory can provide guidance for automatic tuning of the hyperparameter which characterizes the time scale for the dynamics of the estimator. By attenuating the noise from both the cross-sectional and time-series dimensions, we empirically demonstrate the superiority of our estimator over competing estimators that are based on exponentially-weighted and uniformly-weighted covariance matrices.

Related papers

• Statistical Inference in Classification of High-dimensional Gaussian Mixture [1.2354076490479515]
  We investigate the behavior of a general class of regularized convex classifiers in the high-dimensional limit. Our focus is on the generalization error and variable selection properties of the estimators.
  arXiv  Detail & Related papers  (2024-10-25T19:58:36Z)
• Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space [8.971989179518216]
  Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. We utilize tools from optimal transport to generalize the nearest neighbors method to the distributional setting.
  arXiv  Detail & Related papers  (2024-10-17T00:50:17Z)
• A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set [20.166217494056916]
  We propose a principled approach to construct covariance estimators without imposing restrictive assumptions. We show that our robust estimators are efficiently computable and consistent. Numerical experiments based on synthetic and real data show that our robust estimators are competitive with state-of-the-art estimators.
  arXiv  Detail & Related papers  (2024-05-30T15:01:18Z)
• Intrinsic Bayesian Cramér-Rao Bound with an Application to Covariance Matrix Estimation [49.67011673289242]
  This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a smooth manifold. It induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
  arXiv  Detail & Related papers  (2023-11-08T15:17:13Z)
• Regularized Vector Quantization for Tokenized Image Synthesis [126.96880843754066]
  Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. deterministic quantization suffers from severe codebook collapse and misalignment with inference stage while quantization suffers from low codebook utilization and reconstruction objective. This paper presents a regularized vector quantization framework that allows to mitigate perturbed above issues effectively by applying regularization from two perspectives.
  arXiv  Detail & Related papers  (2023-03-11T15:20:54Z)
• TACTiS: Transformer-Attentional Copulas for Time Series [76.71406465526454]
  estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. We propose a versatile method that estimates joint distributions using an attention-based decoder. We show that our model produces state-of-the-art predictions on several real-world datasets.
  arXiv  Detail & Related papers  (2022-02-07T21:37:29Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)
• Covariance Estimation for Matrix-valued Data [9.739753590548796]
  We propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.
  arXiv  Detail & Related papers  (2020-04-11T02:15:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.