Bayesian Value-at-Risk and Expected Shortfall for a Large Portfolio (Multi- and Univariate Approaches)

Studies in Nonlinear Dynamics &Amp; Econometrics

Wróblewska

2017

Abstract:The paper aims at developing new Bayesian Vector Error Correction -Stochastic Volatility (VEC-SV) models, which combine the VEC representation of a VAR structure with stochastic volatility, represented by either the multiplicative stochastic factor (MSF) process or the MSF-SBEKK specification. Appropriate numerical methods (MCMC-based algorithms) are adapted for estimation and comparison of these type of models. Based on data coming from the Polish economy (time series of unemployment, inflation, interest rates, and of PLN/EUR, PLN/USD and EUR/USD exchange rates) it is shown that the models and numerical methods proposed in our study work well in simultaneous modelling of volatility and long-run relationships.

“…Later, the process was employed, e.g. by (Osiewalski and Pajor 2009;Pajor 2011;Pajor and Osiewalski 2012;Osiewalski and Osiewalski 2013).…”

Section: Msf and Msf-sbekk Structures In The Vec Modelmentioning

confidence: 99%

“…Finally, for θ Σ we use the same priors as in (Osiewalski and Pajor 2009;Pajor and Osiewalski 2012).…”

Section: The Prior Distribution and Bayesian Vec-msf Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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VEC-MSF models in Bayesian analysis of short- and long-run relationships

Studies in Nonlinear Dynamics &Amp; Econometrics

Wróblewska

2017

“…Such a result is attributable to the fact that the very same q t factor drives the dynamics of each element of t . The process has been employed in, e.g., Osiewalski and Pajor (2009) and Pajor and Osiewalski (2012).…”

Section: Bayesian Vec Models With Stochastic Volatilitymentioning

confidence: 99%

Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships

Wróblewska

2022

Eurasian Econ Rev

The paper is focused on comparing the forecasting performance of two relatively new types of Vector Error Correction - Multiplicative Stochastic Factor (VEC-MSF) specifications: VEC-MSF with constant conditional correlations, and VEC-MSF-SBEKK with time-varying conditional correlations. For the sake of comparison, random walks, vector autoregressions (VAR) with constant conditional covariance matrix, and VAR-SBEKK models are also considered. Based on daily quotations on three exchange rates: PLN/EUR, PLN/USD, and EUR/USD, where the cointegrating vector may be assumed to be known a priori, we show that in econometric models it can be more important to allow for cointegration relationships than for time-varying conditional covariance matrix.

“…The LN-MSF-SBEKK structure is obtained by multiplying the SBEKK conditional covariance matrix

by a scalar random variable

such that

is a Gaussian AR(1) latent process with autoregression parameter

. The hybrid LN-MSF-SBEKK specification has been recognized in the literature [ 32 , 33 , 34 , 35 ] and proved to be useful in multivariate modeling of financial time series as well as of macroeconomic data [ 36 , 37 , 38 , 39 , 40 , 41 ]. The drawback of the LN-MSF-MGARCH process is that it cannot be treated as a direct extension of the MGARCH process with the Student t conditional distribution.…”

Section: Empirical Illustration: Formal Bayesian Comparison Of Hybrid Msv-mgarch Modelsmentioning

confidence: 99%

New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces

2021

Entropy

Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters.