This thesis recognizes that the premises of standard cointegration (I (1)/I (0) dichotomy) are too restrictive. In this sense, the empirical literature has shown that many economic and financial time series hold long-range dependence in the autocorrelation function but do not precisely exhibit a unit root process, i.e., the long memory process. For this reason, traditional cointegration assumptions that the time series may follow the dichotomy I (0)/I (1) are discard, in favour that they follow a fractional process I (d). We also shed the notion that the error term follows a stationary process (I (0)) in cases of cointegration of both variables. In turn, the rigidity of the traditional approach is overcome in favour of allowing for the series to be cointegrated, and the error term does not necessarily need to be I (0); for example, the error term may be cointegrated in order I(d − b), unlike other techniques that assume the error term is I (0). In this sense, the Fractionally Cointegrated Vector Autorregressive (FCVAR) model is an expansion of the traditional cointegrated VAR (CVAR) model, and it allows to determine the number of equilibrium relations via cointegrating rank testing to estimate memory parameters, long-run cointegrating relations with adjustment parameters, and short-run lagged dynamics. To this end, in the current dissertation, we develop empirical analysis to demonstrate the properties of the time series under the fractional cointegration assumptions. In chapters 2 and 3 we consider the cointegrating relation and adjustment dynamics amongst four major stock markets for the Eurozone, and the five major stock markets for Latin America, respectively. The results evidence that there is a full financial integration in both economic regions, despite of the financial crisis occurred in recent years (this case is studied in chapter 2). The following 4 chapters are devoted to study the term structure of interest rates. Indeed, we summarize an empirical review of the Expectations Hypothesis of the Term Structure (EHTS) aiming to establish the adequate procedures for its measurement by using time series and evidencing the linearity restrictions associated with the traditional approaches used in time series applications on term structure (chapter 4). Furthermore, it is also analyzed the relationship between the European Over Night Index Average (Eonia) rate and 3-month Euribor rate (chapter 5). In chapter 6, we apply a pairwise estimation to a wide sample consisting on 9 different maturities of Treasury Constant interest rates. Otherwise, in chapter 7, we use two historical databases for the USA in order to check the behavior of short- and long-term interest rates. In this four chapters, we demonstrate the fractional properties of the cointegrating relations subject to the EHTS conditions. Additionally, we study how the spread is resulting both interest rates, jointly, analyzing the long memory in the spread that has implications for the monetary transmission mechanism and its effectiveness. In chapter 8, the US debt sustainability is analyzed taking into account the Intertemporal Budget Constraint conditions. We propose different scenarios in which the deficit, i.e., the difference between revenues and expenditures, possess different features, providing significant implications for policy makers. Then, the dominance between revenues and expenditures in the common trend is shown. Finally, in chapter 9, concerning the crude oil market, we test if the relationship between West Texas Intermediate and Brent crude oil is globalized or regionalized. Besides, the difference between both crude oils may be an indicator of forecasting, depending the value of its degree of integration and to finish, the driver of the relationship is defined, which may be an indicator for business operators, arbitrageurs, economic agents and policy makers.
