In the context of the last crisis that the whole world is going through, this study investigates the appropriate models which are not affected from the crisis and represent efficient solutions for an international portfolio investor. Main idea is to highlight the significance of valid forecasting, whose contribution will be of vital importance to avoid the crisis. To this end, the present study is divided in two parts, the theoretical part and the empirical study. The first one analyzes the theory of time series, after retracing the history of relevant studies. In particular, theories of unit roots, cointegration, causality relations and portfolio theories are referred to. The second part analyzes the study. Objective of the study is to examine the behavior of indices such as DAX, CAC 40, FTSE 100, NIKKEI and S&P 500. The data collected refer to a period of 23 years from 1991 up to 2014 on a monthly basis.