The work presented in this dissertation was motivated by the observation that return distributions are not-normally distributed. Under this circumstance, some economic conclusions based on normal and elliptical distributions could be altered. The three chapters of this dissertation investigate various economic problems using copula functions. Chapter one studies the conditional time- varying dependence structure in international stock markets. By comparing the conventionally used linear dependence measure and various alternatives, this paper shows that some differences exist in the time path of dependence. Also, the ̀correlation breakdown' phenomenon clearly shown in the linear measure is not obvious when the copula model is applied. Chapter two examines the impact of changes in the joint distribution of asset returns on investors' portfolio holdings under a CRRA utility function. Using simulated returns with moments set to match actual data, I use linear projections to explore how much of the variation in portfolio weights can be explained by different moments of the return distribution. Simple linear decision rules suggest that expected returns can explain from 70\% to more than 90\% of portfolio holdings. When higher-order moments are added to the decision rule, I find that volatility and skewness are significant and add up to 10\% to the explanatory power of the linear projection, while kurtosis is insignificant in many cases. These results suggest a simple and robust procedure for portfolio choice. This choice is based on linear projections of portfolio weight on the first few (conditional) moments of the return distribution. In a series of out-of-sample forecasting experiments, I find that more information about risk factors may lead people to invest more aggressively. However, this might ruin the performance of the investment, perhaps due to a forecasting error. Chapter three extends the complete conditional coverage test to multivariate cases to address whether different dependence structures are important for evaluating interval forecasts. In an application to international stock returns, I find that a GARCH-$t$ model for the margins passes specification tests in most cases regardless of dependence structure, while the GARCH-Normal does not. However, there is little evidence that any specific dependence structure dominates others