Time-Varying Parameter NARDL (TVP-NARDL)
Time-Varying Parameter Nonlinear Autoregressive Distributed Lag Model · Also known as: TVP-NARDL, time-varying NARDL, rolling NARDL, dynamic asymmetric ARDL
The Time-Varying Parameter NARDL (TVP-NARDL) model extends the Nonlinear ARDL framework by allowing the coefficients on positive and negative partial sums of a regressor to change over time. This combination captures both asymmetric responses and structural instability in long-run and short-run relationships within a single cointegrating specification.
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When to use it
TVP-NARDL is appropriate when theory or visual inspection of rolling estimates suggests that the asymmetric relationship between two integrated variables has shifted over time — for example, exchange-rate pass-through during multiple economic cycles, or oil-price effects on GDP across boom and bust periods. Use it when the sample is long enough to support rolling estimation (typically 60+ observations) and when standard NARDL residuals show parameter instability (CUSUM or Chow tests). Avoid it when the series are short, when there is no prior evidence of time variation, or when the goal is a simple forecasting model rather than structural interpretation, as the additional flexibility can overfit and the results are harder to report concisely.
Strengths & limitations
- Captures both asymmetric and structurally unstable long-run relationships simultaneously.
- Does not require pre-specifying the number or location of structural breaks.
- Yields a visual, period-by-period narrative of how asymmetric effects evolved — useful for policy storytelling.
- Inherits NARDL's bounds-testing approach, so it handles mixed I(0)/I(1) regressors without requiring all series to be integrated of the same order.
- Rolling or Kalman-filter estimation is straightforward to implement in R and Python.
- Requires a sufficiently long time series; short samples produce unreliable coefficient trajectories and wide confidence bands.
- The choice of window width in rolling OLS is arbitrary and can materially affect results; sensitivity analysis across multiple window sizes is necessary.
- Interpreting many time-varying coefficients and multipliers is more complex than reporting a single NARDL estimate.
- State-space / Kalman-filter variants require additional assumptions about the variance of the coefficient innovation process.
- Publication standards for TVP-NARDL are still evolving, so referee expectations vary across journals.
Frequently asked
How is TVP-NARDL different from standard NARDL?
Standard NARDL estimates a single fixed coefficient for positive partial sums and a single coefficient for negative partial sums. TVP-NARDL replaces these fixed numbers with time-indexed trajectories, so the degree of asymmetry can change across the sample period.
What window size should I use for rolling estimation?
There is no universal rule; a common practice is to use 40–60 observations per window and then report sensitivity results for at least two alternative window sizes. The optimal size trades off responsiveness to structural change against estimation precision.
Can TVP-NARDL handle I(2) variables?
No. Like NARDL, the TVP-NARDL framework requires that no variable is integrated of order 2 or higher. Test all series with an ADF or KPSS test before proceeding; I(2) series must be differenced or the model specification is invalid.
Do I still need to run a bounds test?
Yes. You should confirm that a long-run cointegrating relationship exists — for example using the Pesaran, Shin & Smith (2001) bounds F-test on the full sample — before layering time-varying coefficients on top of that relationship.
What software packages support TVP-NARDL?
The 'nardl' and 'MSBVAR' packages in R provide building blocks; rolling OLS is available via 'rollRegres'. Kalman-filter variants can be coded with the 'dlm' or 'KFAS' packages. Python users can combine statsmodels with custom recursive loops.
Sources
- Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In W. Horrace & R. Sickles (Eds.), Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer. link ↗
- Bagnai, A., & Ospina-Rojas, C. A. (2019). Time-varying generalisations of the NARDL model. Economics Letters, 177, 73–76. link ↗
How to cite this page
ScholarGate. (2026, June 3). Time-Varying Parameter Nonlinear Autoregressive Distributed Lag Model. ScholarGate. https://scholargate.app/en/econometrics/time-varying-parameter-nardl
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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