The present work aims at discussing the main theoretical aspects related to the occurrence of long memory processes and its respective application in economics and finance. In order to discuss the main theoretical aspects of its occurrence, it is worth starting from the complex systems approach and emergent phenomena, keeping in mind that many of these are computationally irreducible. In other words, the current state of the system depends on all previous states, in such a way that any change in the initial configuration must cause a significant difference in all posterior states. That is, there is a persistence of information over time-this is a concept directly related to long memory processes. Hence, based on complex systems simulations, three factors (possibly there are many others) were related to the rise of long memory processes: agents' heterogeneity, occurrence of large deviations from the steady states (in conjunction with the motion laws of each system) and spatial complexity (which must influence on information propagation and on the dynamics of agents competition). In relation to the applied knowledge, first it is recognized that the explanatory factors for the rise of long memory processes are common to the structures/characteristics of real markets and it is possible to identify potential stylized facts when filtering the long memory components from time seriesa considerable part of information present in time series is a consequence of the autocorrelation structure, which is directly related to the specificities of each market. Given that, in this thesis was developed a new risk contagion technique that does not need any further intervention. This technique is basically given by the calculation of rolling correlations between long memory filtered series of the conditional variances for different economies, such that these filtered series contain the stylized facts (risk peaks), free from possible overreactions caused by market idiosyncrasies. Then, based on the identification of risk contagion episodes related to the 2007/2008 Subprime Crisis in the U.S. and its respective contagion to the Brazilian economy, it was filtered out from the conditional variance of the Brazilian assets (which are an uncertainty measure) aiming at eliminating the contagion episodes and, consequently, it was made a counterfactual projection of what would have happened to the Brazilian economy if the risk contagion episodes had not occurred. Moreover, in conjunction with the evolutionary trend of the Brazilian economy prior to the crisis, it is possible to conclude that 70% of the economic crisis posterior to the 2008 events was caused by macroeconomic policies and only 30% is due to the effects of risk contagion episodes from the U.S.