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This paper focuses on Greek labour market dynamics at a regional base, which comprises of 16 provinces, as defined by NUTS levels 1 and 2 (Eurostat, 2008), using Markov Chains for proportions data for the first time in the literature. We apply a Bayesian approach, which employs a Monte Carlo Integration procedure that uncovers the entire empirical posterior distribution of transition probabilities from full employment to part employment, unemployment and economically unregistered unemployment and vice a versa. Our results show that there are disparities in the transition probabilities across regions, implying that the convergence of the Greek labour market at a regional base is far from being considered as completed. However, some common patterns are observed as regions in the south of the country exhibit similar transition probabilities between different states of the labour market.

We examine a decision-theoretic Bayesian framework for the estimation of Sharpe Style portfolio weights of the MSCI sector returns. Following van Dijk and Kloek (1980) an appropriately defined prior density of style weights can incorporate non-negativity and other constraints. We use factor-mimicking portfolios as proxies to global style factors such as Value, Growth, Debt and Size. Our computational approach is based on Monte Carlo Integration (MCI) of Kloek and van Dijk (1978) for the estimation of the posterior moments and distribution of portfolio weights. MCI provides a number of advantages, such as a flexible choice of prior distributions, improved numerical accuracy of the estimated parameters, the use of inequality restrictions in prior distributions and exact inference procedures. Our empirical findings suggest that, contrary to existing evidence, style factors do explain the MSCI sector portfolio returns for the particular sample period. Further, non-negativity constraints on portfolio weights were found to be binding in all cases.

We present a new, full multivariate framework for modelling the evolution of conditional correlation between financial asset returns. Our approach assumes that a vector of asset returns is shocked by a vector innovation process the covariance matrix of which is timedependent. We then employ an appropriate Cholesky decomposition of the asset covariance matrix which, when transformed using a Spherical decomposition allows for the modelling of conditional variances and correlations. The resulting asset covariance matrix is guaranteed to be positive definite at each point in time. We follow Christodoulakis and Satchell (2001) in designing conditionally autoregressive stochastic processes for the correlation coefficients and present analytical results for their distribution properties. Our approach allows for explicit out-of-sample forecasting of conditional correlations and generates a number of observed stylised facts such as time-varying correlations, persistence and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). We also study analytically the co-movement between the elements of the asset covariance matrix which are shown to depend on their persistence parameters. We provide empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield which supports our theoretical arguments.