Applied Time Series, Part 2: Multivariate Models, Cointegration, and Dynamic Econometrics

Move from one series to systems of series that move together. This is Part 2 of the two-part Applied Time Series sequence; its prerequisite is Part 1, "Applied Time Series: Statistics and Econometrics of Data with Memory", whose toolkit — stationarity and unit-root testing, ARIMA/SARIMA, and rolling-origin evaluation against naive benchmarks — is assumed throughout and used freely from the first lab. The course takes students from the univariate ARIMA world of Part 1 into intermediate econometrics: dynamic regression done right (distributed lags, ARDL models, long-run multipliers, and HAC inference), vector autoregressions with Granger causality, impulse response functions, and forecast error variance decomposition, and then the course's central arc — cointegration and error correction. Students learn why some nonstationary series share a common stochastic trend, test for it with Engle-Granger residual methods, the ARDL bounds test, and the Johansen procedure, and model it with single-equation ECMs, unrestricted ECMs (UECM), and full vector error correction models (VECM), always reading the economics — long-run equilibria, adjustment speeds, and half-lives — off the estimates. Two further intermediate staples complete the toolkit: ARCH/GARCH models for volatility clustering in financial returns, and structural-break diagnostics (Chow, CUSUM, Bai-Perron, rolling estimation) for parameter instability. Labs run in Python (statsmodels, arch) on quarterly US macro data, genuinely cointegrated market pairs (WTI-Brent crude, the Treasury term structure), daily S&P 500 returns, and a synthetic multivariate suite with known parameters so every rank test, adjustment coefficient, and GARCH fit can be scored against truth. The course closes with a capstone that runs the full decision tree — unit roots, then cointegration, then model choice among ARDL, VAR, and VECM — through structural analysis and honest out-of-sample evaluation against univariate benchmarks from Part 1. The organizing theme: in a multivariate world, the long run and the short run are different objects, and error correction is the bridge between them.

  • Level: intermediate
  • Duration: 10 weeks
  • 11 sections
  • Price: $50

Topics: vector autoregression, VAR, Granger causality, impulse response function, forecast error variance decomposition, Cholesky identification, structural VAR, cointegration, common stochastic trend, Engle-Granger test, error correction model, ECM, unrestricted error correction model, UECM, ARDL, bounds test, long-run multiplier, dynamic multiplier, Johansen test, trace statistic, VECM, adjustment coefficient, weak exogeneity, superconsistency, spurious regression, HAC standard errors, Newey-West, Breusch-Godfrey test, ARCH, GARCH, volatility clustering, leverage effect, value at risk, structural breaks, Chow test, CUSUM, Bai-Perron, rolling estimation, Diebold-Mariano test, forecast combination, statsmodels, arch package

What's inside

  1. Applied Time Series, Part 2: Multivariate Models, Cointegration, and Dynamic Econometrics
  2. Chapter 1: From One Series to Many: Dynamic Regression and the Multivariate Mindset
  3. Chapter 2: Distributed Lags and ARDL: Dynamics in a Single Equation
  4. Chapter 3: Vector Autoregressions: Modeling Systems of Series
  5. Chapter 4: Structural Analysis: Impulse Responses and Variance Decomposition
  6. Chapter 5: Cointegration: Shared Trends and Long-Run Equilibrium
  7. Chapter 6: Error Correction: ECM, UECM, and the ARDL Bounds Test
  8. Chapter 7: System Cointegration: The Johansen Procedure and VECM
  9. Chapter 8: Volatility: ARCH, GARCH, and the Second Moment
  10. Chapter 9: Structural Breaks and Parameter Instability
  11. Chapter 10: The Econometrician's Workflow: Model Choice, Forecast Comparison — Capstone

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