Introduction

• Introduction to the course. Conditional expectations and their features.
• Multiple linear regression analysis: Ordinary Least Squares (OLS) estimator.
• Finite Sample properties of OLS estimator.
• Finite Sample inference.
• OLS asymptotics and large sample inference.
• Specification tests and model selection.
   

Introduction to multivariate time series

• Stationarity, ergodicity. Moments. Linear processes. Martingales. Law of Large Numbers and Central Limit Theorems.
   

Vector Autoregressive (VAR) models for stationary data

• Specification and assumptions. Alternative representations of the model. Estimation (OLS, GLS, SUR, MM, ML) and inference. Stationarity conditions. Moving average (MA) representation. Inference on the MA representation. Forecasting.
   

Introduction to non-stationary time series

• Unit roots and permanent shocks. Integrated processes. Unit root tests and stationarity tests: ADF, PP, KPSS. Cointegration and common trends.
   

Cointegration in VAR models

• Error correction mechanism (ECM) representation of the VAR. Cointegration in VAR(1) models and in the general case. Granger representation theorem. Estimation (RRR, ML) of a cointegrated VAR model. Determination of the cointegration rank. Testing hypotheses on the long run equilibrium and on the short run adjustment.
   

Structural VAR (SVAR) models

• Primitive shocks: identification (Choleski). C form of the SVAR. A-B forms. Identification through long run restrictions (Blanchard-Quah). Relation with systems of simultaneous equations. Estimation and inference.
   

Applications of VAR models

• Forecasting. Impulse Response Functions. Variance Decomposition.

The assessment consists of:

1. A take-home COURSEWORK to be assigned by the lecturer.
2. FINAL WRITTEN EXAM (short-answer, proofs, and numerical questions) based on the material in the syllabus and in the coursework.

Students must pass both coursework and final written exam.