Small sample properties of unrestricted and restricted canonical correlation estimators of cointegrating vectors for panel vector autoregressive process are considered when the cross-sectional dependencies occur in the process generating nonstationary panel data. It is shown that the unrestricted Box-Tiao estimator is slightly outperformed by the unrestricted Johansen estimator if the dynamic properties of the underlying process are correctly specified. The comparison of performance of the restricted canonical correlation estimator of cointegrating vectors for the panel VAR and for the classical VAR applied independently for each cross-section reveals that the latter performs better in small samples when the cross-sectional dependence is limited to the error terms correlations, even though it is inefficient in the limit, but it falls short in comparison to the former when there are cross-sectional dependencies in the short-run dynamics and/or in the long-run adjustments.
We apply Bayesian inference to estimate transformation matrix that converts vector of industry outputs from NACE Rev. 1.1 to NACE Rev. 2 classification. In formal terms, the studied issue is a representative of the class of matrix balancing (updating, disaggregation) problems, often arising in the field of multi-sector economic modelling. These problems are characterised by availability of only partial, limited data and a strong role for prior assumptions, and are typically solved using bi-proportional balancing or cross-entropy minimisation methods. Building on Bayesian highest posterior density formulation for a similarly structured case, we extend the model with specification of prior information based on Dirichlet distribution, as well as employ MCMC sampling. The model features a specific likelihood, representing accounting restrictions in the form of an underdetermined system of equations. The primary contribution, compared to the alternative, widespread approaches, is in providing a clear account of uncertainty.
The first so-called hybrid MSV-MGARCH models were characterized by the conditional covariance matrix that was a product of a univariate latent process and a matrix with a simple MGARCH structure (Engle’s DCC or scalar BEKK). The aim was to parsimoniously describe volatility of a large group of assets. The proposed hybrid models, similarly as pure MSV specifications (and other models based on latent processes), required the Bayesian approach equipped with efficient MCMC simulation tools. The numerical effort has payed – the hybrid models seem particularly useful due to their good fit and ability to jointly cope with large portfolios. In particular, the simplest hybrid, now called the MSF-SBEKK model, has been successfully used in many applications. However, one latent process may be insufficient in the case of a highly heterogeneous portfolio. Thus, in this study we discuss a general hybrid MSV-MGARCH model structure, showing its basic characteristics that explain greater flexibility of such hybrid structure with respect to the corresponding MGARCH class. From the empirical perspective, we advocate the GMSF-SBEKK specification, which uses as many latent processes as there are relatively homogeneous groups of assets. We present full Bayesian inference for such models, with the use of an efficient MCMC simulation strategy. The approach is used to jointly model volatility on very different markets. Joint modelling is formally compared to individual modelling of volatility on each market.
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