| Week | Topics | Study Materials | Materials |
| 1 |
Week 1: Introduction to Time Series Data and Its Importance
• What is a time series? Examples across disciplines
• Types of time series: univariate, multivariate, panel vs. pure time series
• Temporal dependence vs. cross-sectional independence
• Software introduction (e.g., R or Stata)
• Assignment: Exploratory analysis of a real-world time series dataset
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| 2 |
Week 2: Graphical and Numerical Description of Time Series
• Trend, seasonality, cycles, irregular components
• Decomposition methods
• Autocorrelation (ACF) and Partial Autocorrelation (PACF)
• Lab: Plotting and interpreting ACF/PACF in software
• Reading: Chapter from Cryer & Chan or Hamilton
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| 3 |
Week 3: Stationarity and Transformations
• Strict vs. weak stationarity
• Transformations to achieve stationarity (differencing, log, seasonal adjustment)
• White noise and random walks
• Assignment: Determine stationarity with plots and transformations
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| 4 |
Week 4: Unit Root Tests
• Dickey-Fuller and Augmented Dickey-Fuller (ADF) tests
• Phillips-Perron and KPSS tests
• Structural breaks and the problem of spurious regression
• Lab: Unit root testing on macroeconomic or financial data
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| 5 |
Week 5: AR, MA, and ARMA Models
• AR(p) and MA(q) processes
• Conditions for stationarity and invertibility
• Model selection using AIC, BIC
• Hands-on: Estimating ARMA models using real data
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| 6 |
Week 6: ARIMA and SARIMA Models
• Integrating ARMA with differencing › ARIMA(p,d,q)
• Seasonal components: SARIMA(p,d,q)(P,D,Q)[s]
• Box-Jenkins methodology
• Assignment: Fit ARIMA/SARIMA model to a macroeconomic indicator
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| 7 |
Week 7: Model Diagnostics and Forecasting
• Residual diagnostics (ACF, Ljung-Box, Q-statistic)
• Out-of-sample forecasting
• Forecast accuracy metrics: MSE, RMSE, MAE
• Lab: Model fitting and forecast evaluation
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| 8 |
Week 8: Midterm + Practical Review Session
• In-class or take-home Midterm Exam
• Optional Review Lab: Model implementation challenge with feedback
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| 9 |
Week 9: Vector Autoregression (VAR)
• When and why to use VAR
• Impulse response functions (IRF)
• Variance decomposition
• Application: Analyzing economic indicators (e.g., GDP and inflation)
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| 10 |
Week 10: Cointegration and Error Correction Models
• Engle-Granger and Johansen tests
• Long-run equilibrium and short-run dynamics
• Error correction mechanism (ECM)
• Lab: Cointegration tests using economic datasets
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| 11 |
Week 11: Granger Causality and Structural VARs
• Granger causality testing: definition and limitations
• SVAR identification strategies
• Assignment: Apply Granger causality to real-world economic or financial data
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| 12 |
Week 12: Time-Varying Volatility: ARCH and GARCH Models
• Heteroskedasticity in time series
• ARCH(q), GARCH(p,q) models
• Applications in finance and forecasting volatility
• Lab: Estimating GARCH models with asset returns
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| 13 |
Week 13: Advanced Topics and Model Selection
• Structural breaks and regime-switching models
• Model comparison and robustness checks
• Generalized Method of Moments (GMM) introduction
• Assignment: Research project outline and model proposal
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| 14 |
Week 14: Student Project Presentations + Course Wrap-Up
• Final presentations of empirical time series analysis projects
• Peer and instructor feedback
• Synthesis of theoretical and applied components
• Final review and Q&A
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