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Time Series Econometrics

Class at Faculty of Social Sciences |


I.          Basics of time series analysis

·         Stationarity and ergodicity. Linear processes. Lag operator.

·         Innovations and Wold decomposition. AR, MA, ARMA, ARIMA.

·         Trend stationarity and difference stationarity.

·         Nonlinear processes. Processes with time-varying parameters.  

II.        Modeling methodology and model selection

·         Structural and non-structural time series modeling.

·         Object of dynamic modeling: conditional mean, conditional variance, conditional quantile, conditional direction, conditional density.

·         Model selection: diagnostic testing, information criteria and prediction criteria. Model confidence sets.

·         General-to-specific and specific-to-general methodologies. Data mining.

·         Predictability and testing for predictability.  

III.       Modeling conditional mean

·         Stationary AR models: properties, estimation, inference, forecasting.

·         Stochastic and deterministic trends, unit root testing. Brownian motion, FCLT.

·         Nonlinear autoregressions: threshold autoregressions, smooth transition autoregressions, Markov switching models, state-space models.

·         Stationary VAR models: properties, estimation, analysis and forecasting. Nonlinear VAR.

·         Spurious regression, cointegrating regression, and their asymptotics. Engle-Granger test.  

IV.       Modeling conditional variance and volatility

·         The class of ARCH models: properties, estimation, inference and forecasting.

·         Extensions: IGARCH, ARCH-t. Time-varying risk and ARCH-in-mean.

·         Multivariate GARCH: vech, BEKK, CCC, DCC, DECO. Variance targeting.

·         Other measures of financial volatility: RiskMetrics, ranges, realized volatility.

·         MEM models for RV and ranges. HAR models for RV. Models for jumps.  

V.         Other topics on modeling and forecasting

·         Ultra-high frequency data models: ACD, UHF–GARCH.

·         Modeling and forecasting conditional density. ARCD modeling.

·         Multivariate dynamic densities. Copula machinery.

·         Modeling and forecasting direction-of-change. Directional predictability.

·         Modeling and forecasting conditional quantiles. Value-at-risk. CAViaR model.

·         Generalized autoregressive score models. MIDAS models.  

VI.       Analysis of structural stability

·         Identification, estimation and testing for structural breaks. Andrews and Bai-Perron tests.

·         Retrospection and monitoring for structural stability. CUSUM and other sequential tests.


Course requirements, grading, and attendance policies

• The course presumes reading of textbooks and publications, as well as practical computer work with real data.

• There will be weekly home assignments combining theoretical exercises and empirical practice (20% of the course grade).

• One will need programming econometric software to do empirical exercises. Julia, Python, R, MATLAB, GAUSS and other options are acceptable whenever appropriate.

• One may do empirics using low-level programming and get up to the exercise’s full credit (and master the techniques), or, alternatively, utilize embedded high-level commands/libraries and get up to 25% of the exercise’s full credit (and most likely not learn relevant techniques).

• There will be a presentation/mini-lecture (30-40 minutes) on a particular topic assigned far in advance (20% of the course grade).

• There will be a midterm and a final exam (30% of the grade each).

• All the above components are mandatory (two home assignments are excused – for this count but not for the score) for getting a passing grade.

• Discussion sections will be devoted to solving problems and discussing relevant (both theoretical and applied) literature. Active participation in discussion sections will be awarded by up to bonus 10% of the course grade.

Academic integrity policy

Cheating, plagiarism, and any other violations of academic ethics at CERGE-EI are not tolerated.