This dissertation presents a set of econometric tools to uncover the mechanism of credit and financial contagion. First, a nonparametric Granger causality test for continuous time point process data is proposed. The test delivers inference results that are robust to model misspecifications. Applying the test to the point process data of Chapter 11 filings by U.S. corporations and negative shocks of major stock indices, the dissertation provides evidence for credit contagion across different sectors of the economy, as well as financial contagion across international stock markets. Second, a diagnostic checking procedure for parametric multivariate point process models is studied. The metholodogy equips empirical researchers with a portmanteau test in the crucial step of model validation after estimating a proposed parametric model.