Singular Conditional Autoregressive Wishart Model for Realized Covariance Matrices

Alfelt, Gustav; Bodnar, Taras; Javed, Farrukh; Tyrcha, Joanna

doi:10.1080/07350015.2022.2075370

Cited by 3 publications

(4 citation statements)

References 66 publications

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“…Various machine learning methods employ Wishart distributions to represent covariance patterns in multivariate data and evaluate Rayleigh fading MIMO wireless channel performance in wireless communications [9][10]In finance, Wishart-based covariance forecasts improve portfolio risk assessment [11]. Wishart-based stochastic volatility models are used to analyze changes in financial time series covariance matrices [12].…”

Section: Introductionmentioning

confidence: 99%

Exploring Multivariate Statistics: Unveiling the Power of Eigenvalues in Wishart Distribution Analysis

Makled,

Cheng

2024

Preprint

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Energy distance is used to eigenvalue distributions in this new Wishart distribution study, providing a new perspective on high-dimensional data. Multivariate statistics relies on Wishart distribution to explain covariance matrices. This analysis shows how degrees of freedom and covariance matrix configurations affect eigenvalue dispersion. We use energy distance based on eigenvalue distributions to assess Wishart distribution differences without the "curse of dimensionality" via extensive simulation simulations. This approach improves measurement accuracy and processing efficiency in distribution comparisons and enables new analytical pathways in scientific fields that need data covariance comprehension. Our results show that degrees of freedom and matrix structure considerably affect energy distances, expanding the theoretical framework and practical applications of statistical models.

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Section: Introductionmentioning

confidence: 99%

Exploring Multivariate Statistics: Unveiling the Power of Eigenvalues in Wishart Distribution Analysis

Makled,

Cheng

2024

Preprint

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“…The well-known arbitrage pricing theory (APT) proposed by Ross (1976, 1977) shows that the excessive return of assets has a certain relationship with specific factors through a special linear model. In this context, multi-factor models have been widely used and studied, (Aguilar & West, 2000; Alfelt et al, 2022; Bai, 2003; Chamberlain, 1983; Engle & Watson, 1981; Fan et al, 2008). Thanks to these multi-factor models, if several factors can capture the cross-sectional risks completely, the number of parameters to be estimated in the covariance matrix can be reduced significantly (De Nard et al, 2021; X.…”

Section: Introductionmentioning

confidence: 99%

A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Jin

Yuan

2023

Sage Open

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Covariance matrix estimation plays a significant role in both in the theory and practice of portfolio analysis and risk management. This paper deals with the available data prior to developing a factor model to enhance covariance matrix estimation. Our work has two main outcomes. First, for a general linear model with unknown prior parameters, a class of best linear empirical Bayes estimators is established through two kinds of architectures to improve the estimation accuracy by utilizing additional data prior. The theoretical results indicate two key points: the proposed estimators are equivalent to the linear minimum mean-square error estimator when complete or sufficient partial data prior are provided; and the proposed estimators perform better than the optimal weighted least squares method, which ignores the data prior in each situation. Second, the proposed estimators are used for calculating a high-dimensional covariance matrix through factor models. The numerical example and the simulation results verify the effectiveness of our methods.

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“…where μ is a p-dimensional mean vector of the asset returns, is a p × p symmetric positive definite covariance matrix of the asset returns, the coefficient α > 0 describes the investors' risk aversion, 1 r f denotes the rate of a risk-free asset and 1 p is a p-dimensional vector of ones. We allow for short sales and, therefore, some weights can be negative.…”

Section: Introductionmentioning

confidence: 99%

“…As such, the assumption of a constant covariance might only hold for limited periods of time, hence limiting the amount of data available for estimation. Many applications consider portfolios of large dimensions, containing up to 50, 100 or even 1000 assets (see, e.g., [41,26,34,2,20,16,22,5,12,1]). If returns are measured on weekly or monthly intervals, data reaching back several decades might be required to ensure p ≤ N. Unless the considered assets can be assumed to have a constant covariance matrix over very long time periods, data spanning such long time intervals is not suitable to use in the estimation, or might simply not be available.…”

Section: Introductionmentioning

confidence: 99%

On the mean and variance of the estimated tangency portfolio weights for small samples

Alfelt¹,

Mazur²

2022

Modern Stochastics: Theory and Applications

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In this paper, a sample estimator of the tangency portfolio (TP) weights is considered. The focus is on the situation where the number of observations is smaller than the number of assets in the portfolio and the returns are i.i.d. normally distributed. Under these assumptions, the sample covariance matrix follows a singular Wishart distribution and, therefore, the regular inverse cannot be taken. In the paper, bounds and approximations for the first two moments of the estimated TP weights are derived, as well as exact results are obtained when the population covariance matrix is equal to the identity matrix, employing the Moore–Penrose inverse. Moreover, exact moments based on the reflexive generalized inverse are provided. The properties of the bounds are investigated in a simulation study, where they are compared to the sample moments. The difference between the moments based on the reflexive generalized inverse and the sample moments based on the Moore–Penrose inverse is also studied.

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Singular Conditional Autoregressive Wishart Model for Realized Covariance Matrices

Cited by 3 publications

References 66 publications

Exploring Multivariate Statistics: Unveiling the Power of Eigenvalues in Wishart Distribution Analysis

Exploring Multivariate Statistics: Unveiling the Power of Eigenvalues in Wishart Distribution Analysis

A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

On the mean and variance of the estimated tangency portfolio weights for small samples

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