High-Dimensional Cointegration and Impulse Response Harness

Role: Lead Financial Econometrician and Quantitative Macro-Modeler

Context

• System Endogenous Variables: {{time_series_variables}}
• Model Order Selection Rule: {{lag_order_criterion}}
• Rank Determination Critical Value: {{cointegration_rank_threshold}}
• Resampling Iterations: {{bootstrap_replications_count}}
• Dynamics Horizon: {{forecast_horizon_periods}}

Task

Develop an industrial-grade, object-oriented Python script utilizing statsmodels and numpy to ingest multivariate time series, evaluate integration orders, estimate a Vector Error Correction Model (VECM), and output orthogonalized, bootstrapped impulse response functions with empirical confidence bands.

Method

1. Define an ingest module that validates stationarity using Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests for {{time_series_variables}}.
2. Implement optimal VAR lag length selection algorithm evaluating up to maximum 12 lags guided by {{lag_order_criterion}}.
3. Conduct Johansen cointegration tests (Trace and Max-Eigenvalue) at {{cointegration_rank_threshold}} to determine cointegrating rank $r$.
4. Parameterize and estimate the constrained VECM representation, extracting the adjustment speeds (alpha) and long-run cointegrating vectors (beta).
5. Compute residuals and verify absence of serial autocorrelation using Breusch-Godfrey Lagrange Multiplier tests.
6. Construct a wild/residual bootstrap engine with {{bootstrap_replications_count}} resamples to generate non-parametric confidence bands.
7. Propagate structural shocks across {{forecast_horizon_periods}} to calculate orthogonalized Impulse Response Functions (OIRF).
8. Implement automated validation logging and visualization plotting module using matplotlib.

Constraints

• Code MUST be fully runnable Python 3.10+ wrapped in a modular class structure with type hints and docstrings.
• Data input pipeline MUST NOT fail on missing timestamps, implementing strict forward-fill or interpolation guards.
• All bootstrap loops MUST be vectorized or accelerated using multiprocessing to avoid single-thread bottlenecks.
• MUST validate that cointegration rank $r > 0$ before proceeding to VECM; otherwise, fallback to difference-stationary VAR.

Output format

Deliver the analysis pipeline structured in the following sections:

1. Theoretical Specification: A 150-word mathematical summary outlining the error-correction formulation and identification strategy.
2. Complete Python Script: Well-commented, modular code containing TimeSeriesPreprocessor, VECMEngine, and BootstrapIRF classes with a runnable __main__ demonstration block.
3. Metric Interpretation Key: A markdown guide explaining how to interpret alpha speed vectors and persistent versus transitory IRF trajectories.

Self-review

• Ensure the cointegration test accommodates both deterministic trend and intercept options correctly.
• Verify that the bootstrap engine respects temporal dependence without data leakage.
• Confirm that impulse response confidence bands are computed accurately at 95% and 68% coverage levels based on {{bootstrap_replications_count}}.