0
$\begingroup$

Context: I have variables that are non-stationary at level but are stationary at first difference (at least at lags 0 and 1, but become non-stationary beyond this point). I used a VAR model since all variables had the same order of integration, but the model had numerous problems (autocorrelation, heteroscedasticity, non-normal residuals).

So, I tried an ARDL model with the non-stationary data (i.e., not yet differenced) and assigned different lags to the different variables (the ARDL::auto_ardl function in R provided the best lag for each variable based on the AIC criterion), and everything is fine (all diagnostics are okay).

My concern is that apart from Shreshta & Bhatta "Selecting appropriate methodological framework for time series data analysis" (2018) and another post I saw here, I cannot find references that allow me to confirm that it is possible to use ARDL on non-stationary data.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

ARDL does not require stationarity. It is possible to use ARDL with integrated time series. Actually, use can have I(0), I(1) and I($d$) with $0<d<1$ in the same ARDL model. See Dave Giles' blog post "ARDL Models - Part II - Bounds Tests" for details.

Improve this answer
$\endgroup$
6
  • $\begingroup$ Thanks for the link it's a little bit clearer now but I'm still confused about something : since all my variables are I(1) I should be able to do the johansen test to verify if there is cointegration or not (Do I test it on the non stationary variables or once they have been differenced ?). Also when you said ARDL can be used with integrated time series : does it mean that I'm supposed to apply the ARDL on the differenced series or it is okay to apply it on the non stationary one ? $\endgroup$
    – Ranto Antonio
    Commented Sep 8 at 5:23
  • $\begingroup$ @RantoAntonio, you carry our the Johansen procedure on I(1) variables, not their first differences. You can use ARDL with I(1) variables without taking their first differences. $\endgroup$
    – Richard Hardy
    Commented Sep 8 at 9:57
  • $\begingroup$ great thanks! one last question please : since there is a cointegration at rank 1, I try an ECM with an R² of 50% while the ardl one reach 92% is it normal ? How can I correct it ? $\endgroup$
    – Ranto Antonio
    Commented Sep 8 at 14:20
  • $\begingroup$ @RantoAntonio, you can only compare $R^2$ values when the dependent variable is exactly the same. In ARDL, I presume you have $y_t$ in levels on the left hand side while in an ECM you have it in first differences on the left hand side. That is incomparable. You can derive the implied $R^2$ from first differences to levels if you take the actual and fitted values for first diffs, cumulatively sum each one and then calculate the squared correlation between them. Anyway, maximizing $R^2$ should probably not be your goal. Consider it as a descriptive thing instead. $\endgroup$
    – Richard Hardy
    Commented Sep 8 at 14:24
  • $\begingroup$ That makes sense. Thank you ^^ $\endgroup$
    – Ranto Antonio
    Commented Sep 8 at 14:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.