We address the challenge of constructing tangency portfolios in the context of short-selling restrictions. Utilizing Bayesian techniques, we reparameterize the asset return model, enabling direct determination of priors for the tangency portfolio weights. This facilitates the integration of non-negative weight constraints into an investor’s prior beliefs, resulting in a posterior distribution focused exclusively on non-negative values. Portfolio weight estimators are subsequently derived via the Markov Chain Monte Carlo (MCMC) methodology. Our novel Bayesian approach is empirically illustrated using the most significant stocks in the S&P 500 index. The method showcases promising results in terms of risk-adjusted returns and interpretability.

In this article, we study the effect of misspecification caused by fitting the target process in the Phase I analysis of the monitoring procedure on the behavior of several types of multivariate exponentially weighted moving average (MEWMA) control charts in the high-dimensional setting. In particular, the classical MEWMA control charts, whose control statistics are based on the exact and asymptotic Mahalanobis distance, are considered together with the novel approaches where the Euclidean distance and the diagonalized Euclidean distance are employed in the construction of control statistics. The high-dimensional distributions of the control statistics are deduced at each time. These results are later used to assess the performance of the considered control charts under misspecification. Both theoretical and empirical findings lead to the conclusion that the control charts based on the Euclidean distance and the diagonalized Euclidean distance are robust to misspecification for moderate dimensions of the data-generating model, whereas they tend to overestimate the in-control average run lengths (ARLs) in the case of larger dimensions. On the other hand, the control schemes based on the Mahalanobis distance are considerably affected by the estimation of the parameters of the target process, and their application results in drastically smaller values of the ARLs, especially when the dimension of the data-generating model is large.

This paper provides a structured overview of the contents of the Special Issue of the Journal of Multivariate Analysis on “Copula modeling from Abe Sklar to the present day,” along with a brief history of the development of the field.

Bayesian inference procedures for the parameters of the multivariate random effects model are derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the Jeffreys priors are assigned to the model parameters. A new numerical algorithm for drawing samples from the posterior distribution is developed, which is based on the hybrid Gibbs sampler. The new approach is compared to the two Metropolis-Hastings algorithms previously derived in the literature via an extensive simulation study. The findings are applied to a Bayesian multivariate meta-analysis, conducted using the results of ten studies on the effectiveness of a treatment for hypertension. The analysis investigates the treatment effects on systolic and diastolic blood pressure. The second empirical illustration deals with measurement data from the CCAUV.V-K1 key comparison, aiming to compare measurement results of sinusoidal linear accelerometers at four frequencies.

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between -study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data -generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated. MSC2020 subject classifications: Primary 62F15, 62H10; secondary 62H12.

We suggest a new method for integrating volatility information for estimating the value-at-risk and conditional value-at-risk of a portfolio. This new method is developed from the perspective of Bayesian statistics and is based on the idea of volatility clustering. By specifying the hyperparameters in a conjugate prior based on two different rolling window sizes, it is possible to quickly adapt to changes in volatility and automatically specify the degree of certainty in the prior. This gives our method an advantage over existing Bayesian methods, which are less sensitive to such changes in volatilities and usually lack standardized ways of expressing the degree of belief. We illustrate our new approach using both simulated and empirical data. The new method provides a good alternative to other well-known homoscedastic and heteroscedastic models for risk estimation, especially during turbulent periods, when it can quickly adapt to changing market conditions.

In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.

In this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite 4+ε, ε>0, moments. Also, the population covariance matrix with unbounded largest eigenvalue can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S&P 500 index.