This dissertation is organized in four chapters. Chapter 1 introduces the methodology used and briefly describes each chapter. Chapters 2 and 3 test for the existence of fractional cointegration relationships with applications to macroeconomic and financial time series. Chapter 4 studies cross-country monetary spillover effects within the Euro Area. Chapter 2 revisits the question whether volatilities of different markets and tradingzones have a long-run equilibrium in the sense that they are fractionally cointegrated. The notion of fractional cointegration allows for long-term equilibria with a higher degree of persistence than allowed for in the standard cointegration framework. We consider the U.S., Japanese and German stock, bond and foreign exchange market to see whether there is fractional cointegration between the markets in one trading zone or for one market across trading zones. Also, the other combinations of different markets in different trading zones are considered. Applying a purely semiparametric approach through the whole analysis shows that fractional cointegration can only be found for a small minority of different cases. Investigating further we find that all volatility series show persistence breaks during the observation period which may be a reason for different findings inprevious studies.Chapter 3 tests for convergence of EMU inflation rates and industrial productiongrowth rates by using the same semiparametric fractional cointegration methodology as in Chapter 2. Over the full sample from 1999:01-2019:12, we find evidence of fractional cointegration in both inflation and industrial production among many country pairs, where nominal convergence does not necessarily imply real convergence and vice versa. Our results suggest some evidence for ''convergence clusters'' among either core or periphery countries in the case of inflation. By contrast, we find more evidence of mixed core-country cointegration pairs for industrial production, where convergence may be driven by trade links. Testing for a break in the persistence structure, the results show evidence of a break in the persistence of both inflation and industrial production during the beginning of the financial crisis in a number of countries. In all cases, persistence is substantially higher after the break, suggesting a higher potential for diverging processes during economic crises. However, in some cases we find a second break marking the end of the crisis period, with persistence back at pre-crisis levels after the second break.Motivated by the results in Chapter 3, Chapter 4 extends the Eurozone framework by constructing a large dataset and investigating the effects of monetary policy on the economy of 12 country members of the Euro Area. The dynamic relations among monetary policy, real economy, prices and the financial market are examined using time-varying parameter factor-augmented VAR models for the period 2000:01-2019:12. Although the transmission mechanism has demonstrated success in the eurozone, we still find asymmetries over time and across core and periphery countries in both real and nominal terms.