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Statistics and Econometrics 3 (ECO-CO-STATSIII)

ECO-CO-STATSIII

Description

This two-part course introduces students to the analysis, modeling, and estimation of time series processes, with a focus on both stationary and nonstationary models. Students will gain a comprehensive understanding of time series methods and their applications, preparing them for both academic research and practical work in fields that require time-dependent data analysis. The first part will focus on the analysis, modelling and estimation of stationary time series processes; while the second part will extend to include non-stationary models. 

Learning outcomes     
Upon successful completion of this course, students will be able to:
•    Demonstrate a comprehensive understanding of key time series concepts, including stationarity, ergodicity, and ARMA processes.
•    Use Maximum Likelihood Estimation (MLE) to estimate ARMA models.
•    Apply model selection criteria such as BIC, AIC and likelihood ratio tests.
•    Estimate and interpret multivariate VAR models, perform Granger causality tests, and analyze impulse response functions and error bands.
•    Apply methods for analyzing nonstationary time series, including the ADF test, cointegration, and methods to address spurious regression.
•    Understand and apply the Kalman filter in state-space models for time series analysis.
•    Perform identification of structural VARs, incorporating cointegration and vector autoregressions into model identification and analysis.

Assessment    
•    Final Exam (80%)
•    Problem Sets (20%)

Module structure

WEEK 1
Basic Time Series Concepts; Maximum Likelihood Estimation
Topics: 
•    Review of difference equations
•    Stationarity
•    Ergodicity
•    ARMA processes
•    Estimation of ARMA models using MLE 
•    Statistical inference

Hamilton (Chapters 1, 3, 5), Lecture notes.

WEEK 2
MLE – Continued; Multivariate VAR Models
Topics: 
•    Likelihood Ratio test
•    Model selection criteria
•    Stationarity in multivariate VAR models
•    Conditional likelihood and OLS estimation for multivariate VAR models
•    Granger Causality

Hamilton (Chapters 5, 11), Lecture notes.

WEEK 3
Multivariate VAR Models – Continued; Models of Nonstationary Time Series
Topics: 
•    Impulse responses
•    Error bands
•    Recursive VARs
•    Serial Correlation
•    HAC

Hamilton (Chapters 11, 17), Hayashi (Chapter 6), Lecture notes.

WEEK 4
Models of Nonstationary Time Series – Continued; Kalman filter
Topics: 
•    ADF test
•    Cointegration
•    Spurious regression
•    Kalman filter – state space representation 

Hamilton (Chapter 13, 17), Lecture notes.

WEEK 5
Identification of Structural VAR
Topics: 
•    Identification of structural VAR

Hayashi (Chapter 6); Vector Autoregressions and Cointegration, Handbook of Econometrics, Vol. 4, Robert F. Engle and Dan McFadden (editors), North Holland, Lecture notes.; Stock, James, H., and Mark W. Watson. 2001. "Vector Autoregressions." Journal of Economic Perspectives, 15 (4): 101–115.


Bibliography and further readings

Main References:
•    Hamilton, J. H. (1994), Time Series Analysis, Princeton University Press
•    Hayashi, F, Econometrics, Princeton University Press
•    Vector Autoregressions and Cointegration, Handbook of Econometrics, Vol. 4, Robert F. Engle and Dan McFadden (editors), North Holland, Lecture notes.
•    Stock, James, H., and Mark W. Watson. 2001. "Vector Autoregressions." Journal of Economic Perspectives, 15 (4): 101–115
 

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