The first essay extends the pioneering cointegration test of Johansen (1991) to allow for structural breaks in a cointegration system. Instead of using usual dummy variables, we utilize a Fourier function to control for an unknown number of multiple breaks in the cointegration system. When we use dummy variables, we need to determine the number of breaks and their locations a priori in each of the equations in the system. However, this challenging task is converted to a simpler task of determining the number of a few cumulative frequencies when we use a Fourier function. The number of parameters to estimate is reduced significantly, which can lead to a good performance of the tests. We also recommend using a fixed value of cumulative frequencies. We provide the limiting distribution of the Johansen-Fourier tests and the corresponding critical values. Monte Carlo simulations show that the new tests display good size and power properties. An empirical application to the Kilian (2009) dataset shows the result of cointegration, while the conventional Johansen cointegration tests indicate no cointegration. The second essay follows the extensive studies on the similarity and synchronization of member states' economic fundamentals and conditions triggered by the formation of the Economic and monetary union in Europe. Similar institutional and economic conditions are considered essential characteristics, implicit targets, and preferred prerequisite qualifications for the Eurozone members, as the optimal currency area theory indicates. This paper analyzes synchronization in five major macroeconomic variables in the European Union using the dynamic factor model. We do not find significant evidence of synchronization in the Eurozone or EU countries. The degree of synchronization in the Eurozone countries is not greater than that in other countries. Also, we find no significant evidence to show that the EU or Eurozone membership has increased synchronization or similarity within the group over time. Instead, we find that synchronization effects are time-dependent; they are more significant during the financial crisis period. The third and final essay analyzes the co-movements of US housing prices using the state level and metropolitan statistical areas (MSA) data. The objective of the study is to examine the significance and time-varying nature of the co-movements from macroeconomic aspects and determine major factors that drive the movements of the housing prices. Dynamic factor models with time-varying loadings and stochastic volatility (DFM-TV-SV) are employed to estimate the national, regional, and state factors. The results show that the national factor is dominant in explaining the movement of housing prices. On average, the national factor accounts for 79 percent of the variation of housing prices, while its significance is the highest during the housing boom and bust periods in many regions and states. Overall, the significance of each factor varies significantly over time and in different regions. The synchronization effects are also time varying and heterogeneous over different regions and states.