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).
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.
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