Time-Varying Parameter Engle-Granger Cointegration
Time-Varying Parameter Engle-Granger Cointegration Model · Also known as: TVP Engle-Granger cointegration, time-varying cointegration, TVP-EG cointegration, varying-coefficient cointegration
Time-varying parameter (TVP) Engle-Granger cointegration extends the classical two-step Engle-Granger framework by allowing the long-run relationship between integrated series to evolve over time. Instead of assuming a fixed cointegrating vector, the cointegrating coefficients are modelled as stochastic processes — typically via a random walk — and estimated with the Kalman filter or related state-space methods.
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When to use it
Use TVP Engle-Granger cointegration when you have two or more I(1) time series that you expect to share a long-run equilibrium, but also suspect that the strength or direction of that relationship has changed over the sample — for instance, across major policy changes, financial crises, or evolving trade regimes. It is preferable to the static Engle-Granger test when Chow tests or rolling-window estimates signal parameter instability. Do not use it when series are stationary in levels (cointegration does not apply), when the sample is short (fewer than ~80 observations), or when you need a fully multivariate cointegration analysis — the Johansen trace test with time-varying parameters is more appropriate in those cases.
Strengths & limitations
- Captures gradual structural change in the long-run relationship without requiring pre-specified break dates.
- Retains the intuitive two-step Engle-Granger logic while adding temporal flexibility.
- The Kalman filter provides efficient, recursive estimates that use all available data at each period.
- Produces a time path of the cointegrating coefficient, giving economically meaningful insight into how the equilibrium relationship evolves.
- Compatible with standard error-correction model inference once cointegration is confirmed.
- Requires relatively long time series (at least 80–100 observations) for the Kalman filter to converge and deliver stable estimates.
- Estimation of the state-equation variance Q is sensitive to starting values and can be poorly identified in small samples.
- The classical Engle-Granger residual test may have low power when coefficients vary substantially, potentially missing genuine cointegration.
- Restricted to bivariate or low-dimensional systems; high-dimensional extensions require the Johansen TVP framework.
- Interpretation of the time-varying cointegrating vector requires care, especially during highly volatile periods.
Frequently asked
How does this differ from the standard Engle-Granger two-step procedure?
The standard Engle-Granger procedure estimates a fixed cointegrating vector by OLS and then tests the residuals for stationarity. The TVP extension replaces the fixed OLS coefficients with state variables that evolve over time, estimated via the Kalman filter, so the long-run relationship is allowed to drift rather than being constant across the whole sample.
How do I choose the variance of the state equation (Q)?
Q is typically estimated by maximum likelihood in the state-space representation. In practice, sensitivity analysis across a range of Q values is recommended. A very small Q yields near-constant coefficients (approaching OLS), while a large Q allows rapid drift. Model selection criteria such as AIC or BIC can guide the choice.
Can I apply this to more than two variables?
The bivariate TVP Engle-Granger approach extends awkwardly beyond two variables because the choice of normalisation and the ordering of variables affects results. For multivariate systems, a time-varying parameter Johansen approach or a VAR-based state-space model is preferable.
What sample size is needed for reliable results?
At least 80–100 observations are generally recommended to allow the Kalman filter to converge and to give the ADF residual test adequate power. With fewer than 60 observations, the filtered coefficient paths can be erratic and the stationarity test unreliable.
Should I use the TVP model or a structural break model?
If prior knowledge or tests (e.g., Bai-Perron) suggest one or two sharp discrete breaks, a split-sample or dummy-augmented cointegration model may be more parsimonious and easier to interpret. The TVP model is preferable when breaks are gradual, frequent, or unknown in timing and number.
Sources
- Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. DOI: 10.2307/1913236 ↗
- Park, J. Y., & Hahn, S. B. (1999). Cointegrating regressions with time varying coefficients. Econometric Theory, 15(5), 664–703. DOI: 10.1017/S0266466699155026 ↗
How to cite this page
ScholarGate. (2026, June 3). Time-Varying Parameter Engle-Granger Cointegration Model. ScholarGate. https://scholargate.app/en/econometrics/time-varying-parameter-engle-granger-cointegration
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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