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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.

Bayesian assessments of value-at-risk and expected shortfall for a given portfolio of dimension n can be based either on the n-variate predictive distribution of future returns of individual assets, or on the univariate model for portfolio volatility. In both cases, the Bayesian VaR and ES fully take into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this (more demanding) multivariate approach and the much simpler univariate approach based on modelling volatility of the whole portfolio (of a given structure).

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

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.

The article estimates the aggregate production function at the World Technology Frontier on the basis of annual data on inputs and output in 19 highly developed OECD countries in 1970-2004. A comparison of results based on Data Envelopment Analysis and Bayesian Stochastic Frontier Analysis uncovers a number of significant discrepancies between nonparametric estimates of the frontier and parametric (Cobb-Douglas and translog) aggregate production functions in terms of implied technical efficiency levels, partial elasticities, returns to scale, and elasticities of substitution.

In the paper, we consider the Box-Cox transformation of financial time series in Stochastic Volatility models. Bayesian approach is applied to make inference about the Box-Cox transformation parameter (λ). Using daily data (quotations of stock indices), we show that in the Stochastic Volatility models with fat tails and correlated errors (FCSV), the posterior distribution of parameter λ strongly depends on the prior assumption about this parameter. In the majority of cases the values of λ close to 0 are more probable a posteriori than the ones close to 1.

This paper examines short-run relationships among the U.S., German and Greek bond markets in times of financial crises. Specifically, the connections among daily and weekly growth rates of the 10-year government bond yields of the U.S., Germany and Greece from July 13, 2006 to January 29, 2016 are considered and an empirical illustration of those, based on the vector autoregressive (VAR) model with stochastic volatility (SV) disturbances, is provided. Finally, sufficient weak and strong exogeneity conditions in the VAR-SV models are tested. Our results indicate that during the time period covered by the analysis, the weekly growth rates of the 10-year U.S. bond yields were not affected by the past growth rates of the 10-year German and Greek bond yields. Contagion effects were absent among all the 10-year bond markets considered. From October 2008 to April 2015 a 'flight to quality' effect between Germany and Greece, as well as between the U.S. and Greece seems to have occurred. Since the strong exogeneity hypothesis of the 10-year US bond yields' weekly growth rates has not been rejected by the data, they can be predicted from the marginal model only, i.e. without taking the German and Greek bond yields into consideration.