I. Introduction: Stationary Time Series

Introduction to stationary time series
ARMA, limit theory for stationary time series, causal relationships, HAC

3–5 Frequency domain analysis
Spectra; filters; transforms; nonparametric estimation
5 Model selection and information
Consistent estimation of number of lags, discussion of non-uniformity and post-selection inferences
II. Mutivariate Stationary Analysis

Definition, estimation: OLS, ML, Granger causality, impulse response functions and variance decompositions

8 Structural VARs
Identification, short term restrictions, long-term restrictions
9 VAR and DSGE models
World decomposition, fundamentality of shocks, do long-run restrictions identify anything
10–11 Factor model and FAVAR
Motivation, principal components, choosing number of static and dynamic factors, structural FAVAR, IV regression with factors
III. Univariate Non-Stationary Processes
12 Asymptotic theory of empirical processes
13–14 Univariate unit roots and near unit root problem
Unit root problem, unit root testing, confidence sets for persistence, tests for stationarity
15 Structural breaks and non-linearity
Testing for breaks with known and unknown dates, multiple breaks, estimating number of breaks
IV. Multivariate Non-Stationary
16–17 Multivariate unit roots and co-integration
Estimating cointegration relations, canonical form
17 Persistent regressors (prediction regression)
Limit theory, Stambaugh correction, nuisance parameter problem, conservative procedures, conditional procedures
V. GMM and related issues
18 GMM and Simulated GMM
GMM estimation and asymptotic theory, testing in GMM setting, simulated method of moments and time series specifics: estimation of covariance structure, initial condition problem, indirect inference
19 Weak IV
What is weak IV?, alternative asymptotic theory, how to detect weak IV, procedures robust to weak IV, unsolved problems.
VI. Likelihood Methods
20–21 Kalman filter and its applications
State-Space models, time varying coefficients
22 ML estimation of DSGE
Stochastic singularities problem, misspecification and quasi-ML, identification
23 Identification and weak identification of DSGE
VII. Bayesian Methods
24 Bayesian concepts
25 Markov Chain Monte Carlo (MCMC)
Metropolis-Hastings, Gibbs sampler, data augmentation
26 Estimation of DSGE models using Bayesian methods