The lectures will revolve around two main sets of statistical problems, with applications to financial data: i) modeling the full, possibly time-varying predictive distribution, for inference on quantiles and higher moments, and ii) modeling and prediction when parameters can change. These questions willbe tackled both within the context of traditional, tightly parameterized statistical models, and within the context of more recent, highly parameterized and flexible models. The first set of problems includes topics such as heteroscedasticity, quantile regression, generalized linear models, mixtures of experts, and extending gradient boosting to model higher moments. The second set of problems includes topics such as modeling long memory, the interaction of nonlinearity and changes in parameters, modeling parameter shifts in small state-space models, and in large, nonparametric models (mostly gradient boosting).