Course 2021-2022 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.

With the purpose of measuring the acquisition of the above-mentioned learning outcomes, the assessment process is based on a written examination and on four problem sets.

The written exam consists of exercises and/or open questions, aimed at assessing students' ability to:

• Apply the analytical tools illustrated during the course.
• Understand the research papers discussed during the course
• Be able to interpret econometric results and understand their economic meaning
• Identify the economic effects of monetary and fiscal policies.
• Translate economic assumption into restrictions on econometric models.

The problem sets consist in exercises to be solved with the software Matlab. They are aimed at assessing students' ability to:

• Learn how to use the software Matlab
• Translate theoretical concepts into practical computer commands

If students hand in the PS, the final grade will be computed according to the formula:

max(written exam grade;0.7*written exam grade+0.3*average grade in 4 PS)

If students do not hand in the PS, the final grade will be the written exam grade.

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.