Time-Varying Parameter Johansen Cointegration
Also known as: TVP Johansen cointegration, time-varying cointegration, TVP-VECM cointegration, rolling Johansen cointegration
Time-varying parameter (TVP) Johansen cointegration extends the classic Johansen framework by allowing the cointegrating vectors and adjustment speeds to evolve over time. It is designed for integrated multivariate time series whose long-run equilibrium relationships are subject to structural change, regime shifts, or gradual parameter drift, common in macroeconomic and financial data.
Key highlights
- Detects time variation in long-run equilibria that a constant-parameter Johansen test would miss or mis-specify.
- Provides interpretable time paths of cointegrating vectors and adjustment speeds, linking breaks to economic events.
- Subsumes the classical Johansen model as a special case when parameters are constant.
- Compatible with rolling-window, recursive, and state-space (Kalman filter) estimation strategies.
- Applicable to multiple cointegrating relationships in systems with three or more variables.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use TVP Johansen cointegration when you have two or more I(1) series and you suspect the long-run equilibrium relationship is not constant — for example across monetary policy regimes, before and after a financial crisis, or when theory predicts a gradually evolving equilibrium. It is also the natural choice when sequential or rolling Johansen tests on the same data show contradictory rank findings across periods. Do not use it when series are stationary or I(2); prefer the standard constant-parameter Johansen test when a stable equilibrium is theoretically motivated and structural-break tests show no evidence of parameter instability.
Strengths & limitations
- Detects time variation in long-run equilibria that a constant-parameter Johansen test would miss or mis-specify.
- Provides interpretable time paths of cointegrating vectors and adjustment speeds, linking breaks to economic events.
- Subsumes the classical Johansen model as a special case when parameters are constant.
- Compatible with rolling-window, recursive, and state-space (Kalman filter) estimation strategies.
- Applicable to multiple cointegrating relationships in systems with three or more variables.
- Computationally intensive, especially in state-space form with many variables; inference relies on simulation or bootstrap critical values.
- Rolling or recursive approaches reduce effective sample size at each sub-window, reducing test power in short series.
- The choice of window length, state-noise covariance Q, or forgetting factor is somewhat arbitrary and can affect conclusions.
- Asymptotic critical values from Johansen (1991) are not directly applicable to TVP versions; sub-sample or bootstrap critical values are required.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How does TVP Johansen differ from simply running Johansen on sub-samples?
Rolling sub-sample tests give a step-wise picture but are discrete and sensitive to window choice. State-space TVP estimation tracks parameter evolution continuously every period using a Kalman filter, exploiting all observations and providing smooth estimates of how the cointegrating vector drifts over time.
Can I use this method if my series appear to be I(2)?
No. Johansen-type cointegration — fixed or TVP — requires series to be I(1). For I(2) systems, use the Johansen I(2) model or differentiate the series once more before analysis.
What software can estimate the TVP Johansen model?
R packages such as 'tsDyn' and 'vars' handle standard Johansen; TVP extensions require state-space packages like 'dlm' or custom Kalman-filter code. MATLAB's Econometrics Toolbox and EViews also support rolling cointegration tests.
How do I choose the window length for rolling Johansen tests?
No universal rule exists. Common practice is to use the shortest window that still provides reasonable power — typically 40 to 80 observations — and to verify robustness by re-running with alternative window lengths. Bootstrap critical values should replace asymptotic ones in short windows.
Is TVP Johansen cointegration the same as threshold cointegration?
No. Threshold cointegration (e.g., threshold VECM) allows different adjustment regimes depending on the size of the error-correction term, but the cointegrating vector itself is typically fixed. TVP cointegration allows the long-run vector to drift continuously over calendar time, addressing gradual structural change rather than regime-switching nonlinearity.
Sources
- 1.Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551–1580.
- 2.Park, J. Y., & Hahn, S. B. (1999). Cointegrating regressions with time varying coefficients. Econometric Theory, 15(5), 664–703.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Time-varying parameter Johansen cointegration. ScholarGate. https://scholargate.app/econometrics/time-varying-parameter-johansen-cointegration