Course 2019-2020 a.y.

• Stationarity.
• Review of ARMA models. Specification and estimation of ARMA.
• Non-invertibilities.
• Non-stationarity.
• Difference stationary vs Trend stationarity.
• Testing for the presence of unit roots: the Dickey-Fuller test.
• Spurious regression.
• Simultaneous equation bias. The problem of identification.
• The Sims’ critique to old macroeconometrics.
• VAR models.
• Granger causality (application: Sims, 1972).
• Structural VAR and identification (applications: Sims, 1980, Blanchard-Quah, 1989 and Gali, 1999 news shocks and non-invertibilities).
• Cointegration (application: King, Plosser, Stock and Watson, 1991).

• Be familiar with the main concepts and tools of time series analysis and being able to use them in other contexts.
• Understand a vast majority of the scientific literature on time-series and macroeconometrics.
• Identify what are the modelling assumptions underlying any structural macroeconometric model.
• Translate the main assumptions in economic theories into restrictions on the empirical statistical model.

• Perform empirical analysis to uncover the effects of shocks in the economy.
• Design a well-functioning VAR forecasting model.
• Communicate effectively the empirical results of his/her analysis.
• Use a well-known programming software, Matlab, to perform different kind of time-series analyses.
• Do empirical analysis in a constructive way and think critically.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Group assignments

The learning experience of this course includes, in addition to face-to-face lectures, a number of classes in the Computer Laboratory, where the software Matlab is introduced. Students hand in 4 problem sets to be solved in groupwork. Problem Sets consist in replicating seminal papers in the literature of Structural VAR. The solution of the Problem Sets is discussed in the Computer Laboratory, where codes and results are shared. Students are encouraged to bring their own views and to share their insights.

To the end of measuring the acquisition of the above-mentioned learning outcomes, the students’ assessment is based on a final written exam.

• The exam consists of a mix of open questions and applied exercises. Attending students can deliver 4 problem sets.
• Problem sets teach students the use of Matlab to perform empirical analysis.
• Successful completion of the problem sets deliver up to 30% of the final grade. The remaining 70% are contributed by the final exam. Alternatively, students who do not wish to hand in the 4 problem sets can take a final written exam (general) that accounts for 100% of the final grad.

The assessment of non-attending students  follows the same rules as the assessment of attending students who do not hand in problem sets: 100% of the grade is set by the performance in the final exam.

The main course material for both attending and non-attending students is:

• L. SALA, Lecture note on Time Series Analysis.
• W. ENDERS, Applied Econometric Time Series, last edition (selected chapters).
• J.D. HAMILTON, Time Series Analysis, Princeton University Press, 1994 (selected chapters).
•  Additional references are suggested during the course.