This paper demonstrates that the class of conditionally linear and Gaussian statespace models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-Switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach.

We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions on the competing copulas: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or non-nested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student-t copula is favored over Gaussian, Gumbel and Clayton copulas.

This paper develops a return forecasting methodology that allows for instability in the relationship between stock returns and predictor variables, for model uncertainty, and for parameter estimation uncertainty. The predictive regression specification that is put forward allows for occasional structural breaks of random magnitude in the regression parameters, and for uncertainty about the inclusion of forecasting variables, and about the parameter values by employing Bayesian Model Averaging. The implications of these three sources of uncertainty, and their relative importance, are investigated from an active investment management perspective. It is found that the economic value of incorporating all three sources of uncertainty is considerable. A typical investor would be willing to pay up to several hundreds of basis points annually to switch from a passive buy-and-hold strategy to an active strategy based on a return forecasting model that allows for model and parameter uncertainty as well as structural breaks in the regression parameters.