Time series models, non-stationarity and co-integration 

-  Some hypotheses and definitions

    Moments of a stochastic process and stationarity concepts

-  Modelling stationary stochastic processes

    The White Noise process

     Wald decomposition theorem and moving average (MA) representations

     Stationary autoregressive (AR) processes

     Mixed processes: ARMA models, maximum likelihood (ML) estimation, specification and forecasting

-  Modelling non-stationary stochastic processes

    Sources of non-stationarity in first and second moments

    Testing for non-stationarity (and stationarity): Augmented Dickey-Fuller, Phillips-Perron and Ng-Perron tests (ADF-PP-NP)

    Filtering and modelling non-stationary processes: Hodrick-Prescott (HP) filter and ARIMA modelling

    Beveridge-Nelson trend-cycle decomposition (BN) - Hamilton's filter (HTCF) 

-  Non-stationarity and cointegration

    Spurious relations: properties of estimators under stationarity, near-stationarity and non-stationarity

    Concept of co-integration (CI)

    Granger representation theorem and error-correction (EC) representation

    Engle and Granger's and Autoregressive Distributed Lag (ARDL)-based EC models (ECMs)

    (Non) CI tests: Cointegration Rank ADF (CRADF), loading coefficients-based and F-based tests

-  Applications

Multivariate time series modelling

-  The Vector-autoregressive model (VAR)

-  The VAR with exogenous variables (VAR-X) and the Vector-autoregressive Distributed Lag model (VARDL)

-  Identification issues: order and rank conditions for identification

-  Estimation and model evaluation

-  Forecasting and policy simulation

-  Applications

Structural VARs

-  Vector Moving Average (VMA) representation of a VAR

   Impulse Response Function (IRF)

   Forecast Error Variance Decomposition (FEVD)

   Historical Decomposition (HD)

-  Identification strategies for structural VARs

   Cholesky decomposition

   A-B model

   Long-run exclusion restrictions

   Set-identification, i.e., sign restrictions

   The structural Vector-Error-correction model (SVEC): Common Trends approach to identification

   VAR identification and instrumental variables

   Proxy (IV)-VARs 

   Applications

Alternative methods for structural time series modelling

-  Local Projection methods (LP) and VARs

   Identification of LPs through IV-GMM

   Identification of LPs through controls and exclusion restrictions

   Applications

-  Machine Learning methods (ML) for prediction and structural modelling

   Basic ML estimators: Ridge, Lasso and Elastic Net

   Predictive performances of ML methods in low and high-dimensional settings

   Lasso-VARs, forecasting, nowcasting

   Causal ML: LP identified through double-Post-Lasso/Elastic Net

   Causal ML: LP identified through Double/Debiased ML (DML)

   Applications

Reading

• Johnston and DiNardo (1996). Econometric Methods IV edition. McGraw-Hill. ch. 9.4, 9.5 and 9.6

• Kilian, L., Lutkephol, H. (2017). Structural Vector Autoregressive Analysis, Cambridge, Cambridge University Press. 

• Lutkephol, H. Kratzig, M. (2005). Applied Time Series Econometrics. Cambridge University Press

• Hamilton, J. (1994). Time Series Econometrics. Princeton University Press

• Further readings and material distributed during the lessons

Econometric/math packages

All the applications will be executed using Python. For some applications, Matlab codes are also available

Background knowledge

• Students participating to the classes should be familiar with the basic topics in univariate and multivariate time series analysis. 

• Basic programming in Python and Matlab.

Lessons 2024-25

• Tue:   Room: 1-D - time: 10:00 a.m - 12 a.m.

• Wed:  Room: 1-D - time: 06:00 p.m - 08 p.m.

• Thu:   Room: 1-D - time: 10:00 a.m - 12 a.m.