The topics covered in this course are:

1. Stationary time series: definition, properties, acf, pacf, examples (white noise, linear processes, ARMA processes), prediction, lag operator polynomials and their invertibility, spectral analysis, statistical inference in parametric and nonparametric models, CLTs and LLNs.
2. Nonstationary time series: ARIMA models with trends and seasonalities, unit root tests.
3. Conditional heteroskedasticity: definitions, features, and properties of GARCH-type models; parameter estimation in GARCH-type models; variations of the basic GARCH model; stochastic volatility and Markov-switching models.
4. Multivariate time series: definition, properties, VARMA models and their estimation; modeling conditional heteroskedasticities; Granger causality, impulse responses and their identification, structural VAR models; cointegration and VEC models, state space models and the Kálmán filter/predictor/smoother, dynamic factor models.
5. Forecasting financial time series (with an applied focus) based on classical methods and methods from statistical learning.

After successfully completing the course, the student will be able

• to understand the theoretical foundation of a large class of modeling strategies for financial time series, covering ARIMA models, volatility models, VAR (vector autoregressive models), VEC (vector error correction models), Kálmán filter and state space models, as well as dynamic factor models,
• to apply these methods to financial data, and
  
• to interpret the output of statistical software (R in particular).

Participants will be trained in

• understanding the mathematical and statistical properties of the models and inference procedures,
• implementing, executing, and interpreting R scripts,
• conducting a small empirical project,

when doing the assignments and presenting them in class.