Time series analysis
A.A. 2020/2021
Obiettivi formativi
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.
Risultati apprendimento attesi
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.
Periodo: Primo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento non può essere seguito come corso singolo. Puoi trovare gli insegnamenti disponibili consultando il catalogo corsi singoli.
Programma e organizzazione didattica
Edizione unica
Periodo
Primo trimestre
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.
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.
Programma
· 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
- 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
Prerequisiti
Basic course of Econometrics or Inferential Statistics.
Metodi didattici
Lessons and classes.
Materiale di riferimento
A Guide to Modern Econometrics - M. Verbeek
Structural Vector Autoregressions - L. Kilian
Structural Vector Autoregressions - L. Kilian
Modalità di verifica dell’apprendimento e criteri di valutazione
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 - ECONOMETRIA - CFU: 6
Lezioni: 40 ore
Docente:
Bacchiocchi Emanuele