I usually teach finance (asset pricing and equilibrium models), quantitative economics (linear algebra and optimization), econometrics, computer science introduction to programming and machine learning (Bishop and Bengio). I am preparing a 60-hour introductory course of time series for PHD students. I would like to mix theoretical and computational issues. Although the student can use any computer language he wants, I will provide all the examples in python.
There are some expected topics that cannot disappear from any time series introductory course for a department of economics:
Prediction and impulse response functions based on ARMA models
Representations (covariance, Wold and spectral)
However, there are others that I am not exactly sure what to include:
Forecasting (machine learning approach?)
Multivariate models (VAR?)
Nonlinear models (??) [TAR (?), Markov Switching (?), Garch Models (?)]
Topics of Monte Carlo and Bootstrapping for time series (?)
Contemporary issues? State of Art issues?
Correct balance between theory and computation.
Can you help me suggesting topics (and references for these topics) that I could include in the course? Are there time-series references such as Wooldridge (Introductory Econometrics: A Modern Approach) or Inzenman (Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning) that use real data that can be used to exemplify the models?