Time-Varying Parameter Toda-Yamamoto Causality
Time-Varying Parameter Toda-Yamamoto Granger Causality Test · Also known as: TVP-TY causality, time-varying Toda-Yamamoto, TVP Granger causality (Toda-Yamamoto), rolling/recursive Toda-Yamamoto causality
The TVP Toda-Yamamoto causality test combines Toda and Yamamoto's (1995) augmented VAR approach — which handles possibly integrated or cointegrated series without pre-testing for unit roots — with time-varying parameters, allowing causal relationships between variables to shift across different periods rather than remaining fixed throughout the sample.
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When to use it
Use TVP Toda-Yamamoto causality when you suspect that causal linkages between time-series variables are unstable across the sample — for example during structural breaks, regime changes, or policy shifts — and when the series may be non-stationary or of uncertain integration order. It is well suited to macroeconomic and financial series where crises or policy interventions plausibly alter causal dynamics. Do not use it with very short time series (fewer than roughly 60 observations), as rolling windows or Kalman-filter estimation becomes unreliable. It is also inappropriate when the research question involves contemporaneous rather than temporal causality, or when the series are clearly stationary and causality is expected to be stable — in those cases, a standard fixed-parameter Granger or Toda-Yamamoto test is simpler and more efficient.
Strengths & limitations
- Handles nonstationary and possibly cointegrated series without requiring pre-testing for the order of integration.
- Detects time-varying and episodic causal relationships that a single fixed-parameter test would miss or average away.
- The augmented-VAR structure preserves the standard chi-squared distribution for the Wald statistic asymptotically.
- Provides an interpretable graphical output (causality path over time) that can be linked to historical events.
- Robust to mild misspecification of the cointegrating rank because estimation is performed in levels.
- Requires a sufficiently long series; short samples produce unreliable time-varying estimates and distorted test sizes.
- Computational burden is higher than a single Toda-Yamamoto test, especially with many variables or tight rolling windows.
- Results can be sensitive to the choice of window length, lag order p, and the assumed maximum integration order d_max.
- Bootstrap critical values should be preferred over asymptotic ones in finite samples, adding to complexity.
- Does not identify the mechanism or direction of structural change — it only signals that causality shifted.
Frequently asked
How is this different from a standard Toda-Yamamoto test?
The standard Toda-Yamamoto test estimates a single Wald statistic over the whole sample and assumes the causal relationship is constant. The TVP version estimates the test statistic for each rolling window or point in time, revealing whether and when the causal link changes — it is the time-series analogue of asking 'has the relationship been stable?'
What is the role of d_max in this method?
d_max is the maximum suspected order of integration among the variables. By including d_max extra lags in the VAR but testing only the first p lags, the procedure ensures the Wald statistic follows a chi-squared distribution asymptotically, even for I(1) or I(2) series, so no pre-testing for cointegration is needed.
How should I choose the rolling window length?
There is no universal rule. A common practice is to use 30–50 percent of the total sample as the minimum window, then check robustness across several window sizes. Shorter windows capture rapid structural changes but produce noisier estimates; longer windows are smoother but may mask sudden breaks.
Should I use asymptotic or bootstrap critical values?
Bootstrap critical values are generally preferred, especially in finite samples and when the series are highly persistent. Asymptotic chi-squared critical values can over-reject the null (find spurious causality) in small or rolling-window samples.
Can I apply this to more than two variables?
Yes. The VAR framework naturally extends to multiple variables. However, as the number of variables grows, the parameter space expands quickly, so you need a longer sample and should consider imposing shrinkage (e.g., a Bayesian TVP-VAR prior) to keep estimates stable.
Sources
- Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1-2), 225-250. DOI: 10.1016/0304-4076(94)01616-8 ↗
- Adebayo, T. S., & Acheampong, A. O. (2022). Modelling the globalization-emissions nexus: Fresh insights from the novel dynamic ARDL simulations and the Toda-Yamamoto causality approaches. Environmental Science and Pollution Research, 29(3), 3825-3840. link ↗
How to cite this page
ScholarGate. (2026, June 3). Time-Varying Parameter Toda-Yamamoto Granger Causality Test. ScholarGate. https://scholargate.app/en/econometrics/time-varying-parameter-toda-yamamoto-causality
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.
- Granger CausalityEconometrics↔ compare
- Toda-Yamamoto CausalityEconometrics↔ compare
- VAR ModelEconometrics↔ compare