A fully Bayesian analysis of seasonal and nonseasonal forms of nonstationarity is presented. The thesis consists of three parts, which are structured as separate research articles. In the first paper a Bayesian approach to model selection in testing regressions for a zero frequency unit root with multiple structural breaks is proposed. For this purpose the number of breaks, the corresponding break dates as well as the number of autoregressive lags are treated as model indicators, whose posterior distributions are computed using a hybrid Markov chain Monte Carlo (MCMC) approach that allows to generate random draws from parameter spaces of varying dimension. The second part of the thesis is devoted to seasonal forms of nonstationarity. Here a Bayesian testing approach for a periodic unit root in the presence of a break at unknown time for quarterly and monthly data is presented and the required posterior distribution is derived.
In addition, a Bayesian F-test is suggested to test for seasonal and nonseasonal unit roots again controlling for a possible break. Instead of resorting to a model selection approach by choosing one particular model specification for testing, a Bayesian model averaging (BMA) approach is proposed to capture the model uncertainty associated with a specic parametrization of the test regression. In the third part of the thesis a Bayesian periodic autoregressive (PAR) model is then utilized for the prediction of quarterly and monthly time series data. A model averaging prediction approach for PAR models of unknown lag orders, number of breaks and break dates is proposed in order to improve the forecasting accuracy compared to conditional approaches. Further the joint posterior distribution of the multistep ahead forecasts is derived and an MCMC approach, based on data augmentation, is presented to generate random draws from the marginal posterior predictive distributions. In each of the three articles a Monte Carlo study is conducted to analyze the presented methods under different data generating processes.
In the first two parts the presented testing approaches are utilized to examine if there is empirical evidence for persistence or hysteresis in the annual unemployment rates of OECD countries.
In the last part of the thesis it is demonstrated how the suggested BMA prediction approach can improve forecasting accuracy compared to conditional, i.e. model selected, Bayesian PAR models using unadjusted monthly unemployment rates of East- and West-Germany and of the 16 German federal states
