In recent years there has been an active debate about long-run predictability of excess asset returns and the existence of potential predictor variables, e.g. the dividend-price ratio. Since it seems intuitive that this ratio does not grow or fall without bound, it is unclear whether adjustments occur via changes of prices or dividends or both. In case of the former one has long-run predicatibility of asset prices. In this project we apply advanced multivariate time series methods that allow for strong persistence in the dynamics of predictor variables and investigate its impact on long-run portfolio choice. Econometrically, this is done by using multivariate long memory models with one or more fractional cointegration relations. Among other things this line of research requires a profound analysis of estimation and testing methods for available sample sizes using computer simulations as well as identifying reliable model selection methods.