EN
IT
Obiettivi Formativi
OBIETTIVI FORMATIVI: Gli studenti apprenderanno conoscenza teorica e capacità avanzate dell'analisi econometrica dei fenomeni economici e finanziari nel tempo.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE: Gli studenti saranno capacità di sviluppare tutte le fasi del processo di una analisi empirica volta all’'analisi e alla previsione delle serie storiche economiche e finanziarie.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE: Gli studenti saranno in grado di capire e utilizzare i principali modelli dinamici usati nella ricerca empirica.
AUTONOMIA DI GIUDIZIO: Gli studenti impareranno a valutare le implicazioni dei risultati statistici per il problema in esame.
ABILITÀ COMUNICATIVE: Gli studenti saranno in grado di comunicare efficacemente risultati delle analisi empiriche basate su dati in serie storiche.
CAPACITÀ DI APPRENDIMENTO: Gli studenti saranno stimolati a sviluppare le loro abilità mediante la lettura di articoli scientifici e l'uso di database specializzati.
Learning Objectives
LEARNING OUTCOMES: Students are expected to gain theoretical knowledge and advanced skills on the econometric analysis of economic and financial phenomena over time.
KNOWLEDGE AND UNDERSTANDING: Students will be able to autonomously develop all the phases of an empirical project aiming at analyzing and forecasting economic and financial time series.
APPLYING KNOWLEDGE AND UNDERSTANDING: Students will be able to understand an apply the main dynamic models that are used in empirical analyses.
MAKING JUDGEMENTS: Students will gain the ability to make judgments about implications of the statistical results for the issue at hand.
COMMUNICATION SKILLS: Students will be able to present and communicate effectively the results of the empirical analyses on time series data.
LEARNING SKILLS: Students will have the ability to develop and increase their skills through the consultation of the published scientific literature and the use of databases and other information.
Prerequisiti
Matematica
Statistica
Modello di regressione lineare
Prerequisites
Mathematics
Statistics
Linear regression model
Programma
Serie storiche univariate:
1) Serie storiche stazionarie e nonstazionarie (prima settimana).
2) Inferenza statistica e previsione (seconda settimana).
3) Radice unitarie in economia e finanza (terza settimana).
Serie storiche multivariate:
4) Stazionarietà e ergodicità; Rappresentazione di Wold multivariata; Modelli VAR (quarta settimana).
5) VAR strutturali (quinta settimana).
6) Cointegrazione (sesta settimana).
Program
Univariate Time Series:
1) Stationary and non-stationary time series (first week)
2) Statistical inference and forecasting (second week)
3) Unit-roots in economics and finance (third week)
Multivariate Time Series:
4) Stationary and Ergodic Multivariate Time Series; Multivariate Wold Representation;
Vector Auto-Regressive (VAR) Models (fourth week)
5) Structural VAR Models (fifth week)
6) Cointegration (sixth week)
Testi Adottati
Hansen, B.E. (2022), Econometrics, Princeton University Press (PDF freely available at GitHub).
Books
Hansen, B.E. (2022), Econometrics, Princeton University Press (PDF freely available at GitHub).
Bibliografia
Cochrane, J.H. (2005), Time Series for Macroeconomics and Finance, Manuscript.
Mills, T.C. & R.N. Markellos (2008), The Econometric Modelling ofFinancial Time Series, 3rd Edition, Cambridge University Press.
Bibliography
Cochrane, J.H. (2005), Time Series for Macroeconomics and Finance, Manuscript.
Mills, T.C. & R.N. Markellos (2008), The Econometric Modelling of Financial Time Series, 3rd Edition, Cambridge University Press.
Modalità di svolgimento
Lezioni e esercitazioni in aula, compiti da svolgere a casa.
Teaching methods
Lesson and practice in class, homework.
Regolamento Esame
La valutazione dello studente prevede una prova ……scritta in cui vengono proposti esercizi sulla teoria e domande di comprensione sugli argomenti del corso. Il voto medio degli esercizi a casa (se svolti) conta per il 20% del voto finale.
Lo studente dovrà dimostrare di aver appreso la conoscenza teorica e le capacità avanzate dell'analisi econometrica dei fenomeni economici nel tempo.
La prova non può essere sostenuta due volte nella sessione invernale.
Exam Rules
The evaluation consists of a written exam that involves theoretical exercises and questions about the topics of the course. The average mark of the homework (if taken) will be weighted for 20% of the overall mark.
The student should demonstrate to have learned the theory and the advanced skills required for the econometric analysis of empirical phenomenons over time.
The exam cannot be taken twice in the winter session.
EN
IT
Obiettivi Formativi
OBIETTIVI FORMATIVI: Gli studenti apprenderanno conoscenza teorica e capacità avanzate dell'analisi econometrica dei fenomeni economici e finanziari nel tempo.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE: Gli studenti saranno capacità di sviluppare tutte le fasi del processo di una analisi empirica volta all’'analisi e alla previsione delle serie storiche economiche e finanziarie.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE: Gli studenti saranno in grado di capire e utilizzare i principali modelli dinamici usati nella ricerca empirica.
AUTONOMIA DI GIUDIZIO: Gli studenti impareranno a valutare le implicazioni dei risultati statistici per il problema in esame.
ABILITÀ COMUNICATIVE: Gli studenti saranno in grado di comunicare efficacemente risultati delle analisi empiriche basate su dati in serie storiche.
CAPACITÀ DI APPRENDIMENTO: Gli studenti saranno stimolati a sviluppare le loro abilità mediante la lettura di articoli scientifici e l'uso di database specializzati.
Learning Objectives
LEARNING OUTCOMES: Students are expected to gain theoretical knowledge and advanced skills on the econometric analysis of economic and financial phenomena over time.
KNOWLEDGE AND UNDERSTANDING: Students will be able to autonomously develop all the phases of an empirical project aiming at analyzing and forecasting economic and financial time series.
APPLYING KNOWLEDGE AND UNDERSTANDING: Students will be able to understand an apply the main dynamic models that are used in empirical analyses.
MAKING JUDGEMENTS: Students will gain the ability to make judgments about implications of the statistical results for the issue at hand.
COMMUNICATION SKILLS: Students will be able to present and communicate effectively the results of the empirical analyses on time series data.
LEARNING SKILLS: Students will have the ability to develop and increase their skills through the consultation of the published scientific literature and the use of databases and other information.
Prerequisiti
Matematica
Statistica
Modello di regressione lineare
Prerequisites
Mathematics
Statistics
Linear regression model
Programma
Serie storiche univariate:
Serie storiche stazionarie e nonstazionarie.
Inferenza statistica.
Radice unitarie in economia e finanza.
Serie storiche multivariate:
Stazionarieta' e ergodicita'.
Rappresentazione di Wold multivariata.
Modelli VAR.
VAR strutturali
Cointegrazione.
Program
Univariate Time Series:
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series:
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Testi Adottati
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Books
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Bibliografia
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Bibliography
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Modalità di svolgimento
Lezioni e esercitazioni in aula, compiti da svolgere a casa.
Teaching methods
Lesson and practice in class, homework.
Regolamento Esame
La valutazione dello studente prevede una prova ……scritta in cui vengono proposti esercizi sulla teoria e domande di comprensione sugli argomenti del corso. Il voto medio degli esercizi a casa (se svolti) conta per il 20% del voto finale.
Lo studente dovrà dimostrare di aver appreso la conoscenza teorica e le capacità avanzate dell'analisi econometrica dei fenomeni economici nel tempo.
La prova non può essere sostenuta due volte nella sessione invernale.
Exam Rules
The evaluation consists of a written exam that involves theoretical exercises and questions about the topics of the course. The average mark of the homework (if taken) will be weighted for 20% of the overall mark.
The student should demonstrate to have learned the theory and the advanced skills required for the econometric analysis of empirical phenomenons over time.
The exam cannot be taken twice in the winter session.
Aggiornato A.A. 2021-2022
Aggiornato A.A. 2021-2022
This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Suggested readings:
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Aggiornato A.A. 2020-2021
Aggiornato A.A. 2020-2021
This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Suggested readings:
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Aggiornato A.A. 2019-2020
Aggiornato A.A. 2019-2020
This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Suggested readings:
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Aggiornato A.A. 2018-2019
Aggiornato A.A. 2018-2019
This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
Textbook:
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley.
Suggested readings:
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Aggiornato A.A. 2017-2018
Aggiornato A.A. 2017-2018
This course aims at providing a sound knowledge of the basic statistical tools for modelling economic and financial time series.
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
List of References
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley .
Aggiornato A.A. 2016-2017
Aggiornato A.A. 2016-2017
Univariate Time Series
Stationary time series: Basic concepts. Stationarity, Total and partial autocorrelation, Ergodicity, Linear stationary processes, ARMA models, Outliers, Forecasting.
Nonstationary time series: ARIMA models, The Beveridge-Nelson Trend-Cycle decomposition, Seasonality,
Statistical inference: Estimation, Identification, Diagnostic checking.
Unit roots in economic and financial time series: Deterministic trends vs. random walks, Unit-roots tests, Impulse response function and measures of persistence
Multivariate Time Series
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
List of References
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley .
Aggiornato A.A. 2015-2016
Aggiornato A.A. 2015-2016
Univariate Time Series
Program
Stationary time series analysis: Basic concepts. Stationarity, autocorrelation, partial autocorrelation.
Linear stationary processes.
Auto-Regressive Moving Average (ARMA) models.
Forecasting.
Nonstationary time series analysis: ARIMA models. Seasonality, The Box-Jenkins approach.
Unit roots in macroeconomic time series: Deterministic trends vs. random walks.
Unit-roots tests.
The Beveridge-Nelson trend-cycle decomposition.
Impulse response function and measures of persistence.
LIST OF REFERENCES
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley .
Multivariate Time Series
PROGRAM
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Auto-Regressive (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
LIST of REFERENCES:
Lütkepohl, H. (2005) "New Introduction to Multiple Time Series Analysis", Springer.
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press
Aggiornato A.A. 2014-2015
Aggiornato A.A. 2014-2015
Univariate Time Series
Program
Stationary time series analysis: Basic concepts. Stationarity, autocorrelation, partial autocorrelation.
Linear stationary processes.
ARMA models.
Forecasting.
Nonstationary time series analysis: ARIMA models. Seasonality, The Box-Jenkins approach.
Unit roots in macroeconomic time series: Deterministic trends vs. random walks.
Unit-roots tests.
The Beveridge-Nelson trend-cycle decomposition.
Impulse response function and measures of persistence.
LIST OF REFERENCES
Brockwell and Davis (2002) Introduction to Time Series and Forecasting, second edition, Springer-Verlag, New York .
Hamilton (1994), Time Series Analysis, Princeton University Press.
Wei (2006) Time Series Analysis: Univariate and Multivariate Methods, second editiom, Addison-Wesley .
Multivariate Time Series
PROGRAM
Stationary and Ergodic Multivariate Time Series
Multivariate Wold Representation
Vector Autoregression (VAR) Models
Identification and Estimation of VAR models
Forecasting
Structural VAR Models
Impulse Response Functions
Forecast Error Variance Decompositions
Shocks Identification Using the Choleski Factorization
The Cointegrated VAR
Maximum Likelihood Inference on the Cointegrated VAR
The Common Trends Representation.
LIST of REFERENCES:
Lütkepohl, H. (2005) "New Introduction to Multiple Time Series Analysis", Springer.
Hamilton, J.D. (1994) "Time Series Analysis", Princeton University Press
Prof.ssa Lucia Leonelli
