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This course is an introduction to modern time series econometrics, with an emphasis on methods designed to deal with “big data” in macroeconomics and finance. The three main subjects of the course are: (i) univariate predictive regressions with many regressors; (ii) dynamic factor models, as a first example of popular multivariate models that can handle large datasets; (iii) Bayesian VARs, as a second example of big data multivariate models, which also represent a bridge between reduced-form and structural models. We will also touch upon several other topics, such as state-space models, Monte Carlo methods, model comparison, and model choice. Along the way, we will discuss applications to nowcasting and forecasting in macroeconomics and finance, portfolio selection, term structure models, scenario analysis, monetary policy transmission, and long-horizon forecasts. A solid background in mathematical statistics is required.