**Instructor:** Ed Herbst ed.herbst@gmail.com | website

**Course Time and Location:** Class will meet once a
week Mondays from 9:30a-12:00 for lecture in ICC 107.

**Course Description:** The course is an introduction to univariate
and multivariate time series models. Time domain methods, including
VAR's, structural VAR's, Bayesian VAR's for linear models and GMM for
non-linear stationary models are covered. An introduction to
non-stationary time series models is given. Frequency domain methods
and their applications to business cycle inference is also
covered. The course starts by introducing basic concepts and
progresses to more complicated models. The course intends to meet two
goals. It provides tools for empirical work with time series data,
mostly for macroeconomic applications and provides a heuristic
introduction into the theoretical foundation of time series models.

**Course Web Page:** Course documents and information are available via
canvas and at http://edherbst.net/teaching/econ-616.

**Prerequisites:** Econ 613 and 614.

**Assessment.** Your grade will be equally weighted based on problems
sets and a final exam.

*Problem Sets:*[50%] There will be approximately 6 problem sets assigned
during the semester. The problem sets are designed to give the
students the opportunity to review, enhance, and extend the
material learned in class. Students are encouraged to form small
study groups, however, each student has to submit his or her own
write-up of the solution. These solutions must be submitted on the
specified due dates.

*Final Exam:*[50%] (take home)

**Programming and Computation.** Macroeconometrics is an intensely
computational field. It is important to be proficient in at least one
interpeted programming language popular in economics. The assignments
will require (some) light programming. I'll say more about this on
the first day of class.

**Course text.** There is no one textbook that exactly matches the
material covered in class. I will make my lecture notes available on
the internet. You should get a copy of citet:Hamilton, which broadly
classical approach to time series analysis (and some Bayesian
analysis).

Other textbooks that you might find helpful are (though I recommend that you take a close look before you purchase any of them):

**General Econometrics:**Amemiya (1984), cite:White2001, cite:Davidson2003, Hayashi (2000)

**Time Series Analysis:**cite:Brockwell_1987, cite:CLK, cite:GrangerNewbold, cite:Harvey1990

**Modern Macroeconometrics:**cite:CanovaBOOK, cite:ChetanDejongBOOK, cite:HerbstSchorfheide2015

**Bayesian Statistics and Econometrics:**cite:Gelman2003, cite:Geweke2005, cite:Koop2003, cite:lancaster2004, cite:Robert1994

*Note:* This course outline is subject to change during the semester!

- Estimation and Serial Dependence, Empirical Measures of Dependency
- Covariance Stationarity, Stationarity and Ergodicity
- Martingales and Martingale Difference Sequences
- Theoretical Properties: Moving Average Processes
- Theoretical Properties: Autoregressive Models

- Analysis of the Deterministic Trend Model: Rates of Convergence, OLS
- Autoregressive Models with a Unit Root
- Testing for Unit Roots
- Unit Roots from the Frequentist and the Bayesian Perspective
- Cointegration and Error Correction Models

- Typical Spectrum of Macroeconomic Time Series
- Spectral Representation for the Linear Cyclical Model
- Spectral Representation for Stationary Processes
- Filters
- Spectral Estimation
- Generalized method of moments and maximum likelihood estimation interpreted as extremum estimation.

- VAR extension of AR(p) model
- Estimation of VARs
- Forecasting with VARs

- Introduction to Bayesian Statistics: Point Estimation, Testing Theory
- Bayesian Analysis of AR Models
- Bayesian Model Selection: Determining the Order of an AR process
- Markov-Chain Monte Carlo Methods to Generate Draws from Posteriors

- Bayesian Interpretation of the Kalman Filter
- Computing likelihood functions for LRE models
- Nonlinear Models: Markov-Switching

- Principal Components Analysis
- Dynamic Factors
- Determining Number of Factors
- Factor Augmented VAR

- Identification
- Algorithms for Inference
- Extensions: MS-VAR, TVP-VAR, Proxy-SVAR

- LRE models as approximations to dynamic stochastic equilibrium (DSGE) models.
- Moment-based Estimation of linear and nonlinear rational expectations models
- Likelihood-based Estimation of LRE models.

- DSGE-VARs
- DSGE-DFM
- Proxy SVAR

- Sequential Monte Carlo for static parameters
- Particle Filtering
- Advanced MCMC