Time Series Analysis

A.Y. 2020/2021
Overall hours
Learning objectives
This course introduces to the time series methods and practices generally used in the analysis of economic and financial time series. We will cover both univariate and multivariate models of stationary and non-stationary time series. The aim of the course is twofold: first to develop a comprehensive set of tools and techniques for analysing various forms of univariate and multivariate time series, and second to acquire knowledge of recent changes in the methodology of econometric analysis of time series.
Expected learning outcomes
At the end of the course students will be able to analyse macroeconomic and financial time series and use them in econometric models. Specifically, students will be familiar with univariate statistical techniques generally used to study the dynamics of a time series, like ARMA and ARIMA models, and the dynamics of their conditional variance, like ARCH and GARCH models. They will be also able to deal with linear regression models using stationary and non-stationary time series, as in the case of cointegration. Finally, students will be familiar with recent methodologies concerning multiequational models, like VARs and Structural VARs. They will be able to specify and estimate the unknown parameters of the equations and use them to investigate about the dynamic and causal impact of macroeconomic and financial shocks on the endogenous variables of the model.
Course syllabus and organization

Single session

Lesson period
First trimester
All information will be posted on the course webpage on http://ariel.unimi.it.

Lectures will take place online in synchronous way on the Zoom (or MSTeams) platform according to the timetable provided by the university. Lectures will possibly be recorded and made available to the students to be followed in an asynchronous way.

The program of the course will not change.

The written exams during the emergency will maintain the same structure of the usual ones and will be organized through the platform Exam.net, with an external supervision by Zoom or MSTeams.
Course syllabus
· Heteroskedasticity and Autocorrelation
- Consequences for the OLS estimator
- Deriving an alternative estimator
- Heteroskedasticity
- Testing for heteroskedasticity
- Autocorrelation
- Testing for first-order autocorrelation
- Alternative autocorrelation patterns
- What to do when you find autocorrelation

· Univariate Time Series Models
- Introduction
- General ARMA processes
- Stationarity and Unit Roots
- Testing for Unit Roots
- Estimation of ARMA models
- Choosing a model
- Predicting with ARMA models
- Autoregressive Conditional Heteroskedasticity
- What about multivariate models

· Multivariate Time Series Models
- Dynamic models with stationary variables
- Models with nonstationary variables
- Spurious regression
- Cointegration and the Engle-Granger approach
- Error Correction Models
- Vector Autoregressive Models

· Structural Vector Autoregressive Models (see Kilian notes, Sections 1 and 2)
- From the reduced form to the structural form
- The Choleski decomposition
- Impulse responses and interpretation of the structural shocks
Prerequisites for admission
Basic course of Econometrics or Inferential Statistics.
Teaching methods
Lessons and classes.
Teaching Resources
A Guide to Modern Econometrics - M. Verbeek
Structural Vector Autoregressions - L. Kilian
Assessment methods and Criteria
Written exam. Only for the first exam just at the end of the course, there is the possibility to choose between the standard written exam and a practical assessment to do at home using and econometric software.
SECS-P/05 - ECONOMETRICS - University credits: 6
Lessons: 40 hours
Professor: Bacchiocchi Emanuele