This course follows the macroeconometrics course of Professor Forni. In Macroeconometrics you have thoroughly studied univariate and multivariate ARMA models, both stationary and non-stationary. ARMA models are linear models. This course has two main objectives. First, we introduce nonlinear models frequently used in macroeconomics, such as Threshold models, Self-exciting threshold models, Smooth transition models. In all these cases, we basically augment a linear time series model with a nonlinear component, whose role is to capture asymmetric behavior of many macroeconomic variable over the cycle. Needless to say, we do not want to use an unnecessarily complicated nonlinear model, if we do not need it. Hence, we introduce a general approach for testing the null hypothesis of no nonlinearities. So that, if we do not reject the null, we can safely rely on our linear model, otherwise we move to estimate the nonlinear model. One of the most important use of time series econometrics is out of sample prediction. We use information on the past and on the present to predict the future. An accurate prediction is crucial for effective economic policy. Different models produce different predictions. Hence, we introduce tools which allow us to evaluate the relative predictive ability of forecasting models. Finally, we conclude with an overview of models for estimating predicting volatility.