# Lag length selection in a dynamic model, ARDL approach to cointegration in R

I want to programme an ARDL approach to cointegration in R. Below is the generic equation: $$\Delta y_t=\beta_0+\sum \beta_i \Delta y_{t-i}+\sum \gamma_k \Delta x_{1,t-k}+\sum \psi_j \Delta x_{2,t-j}+\phi z_{t-1}+\epsilon_t$$ here, $\phi$ is the coefficient of the error correction term, and the lag length of differenced terms vary, they are not equal, i.e. $k\neq j \neq i$. Because of this, I find it hard to determine an optimal lag length for this model. I think the way forward is to use an information criterion, but it will have to be in nested loops and it is not an efficient way of determining lag length.

Do you know of a programme/code/routine or an algorithm that can handle this situation?

• It's probably $z_{t-1}$ rather than $\phi$ that is the error correction term. How is your ARDL model different from the standard VECM? Is the only difference that you allow for $k \neq j \neq i$? Or do you also put extra structure on betas, gammas and deltas (I suppose you should have deltas in the third sum, not gammas) like Koyck or Almon? – Richard Hardy Oct 28 '15 at 19:03
• @RichardHardy, yes, the $3^{rd}$ $\gamma$ is a typo, thanks for pointing it out. Also, yes, $\phi$ is the coefficient of ect. VECM is for multiple cointegrating relations, in this model, you cannot have more than one ect. – mr.rox Oct 28 '15 at 20:07
• Splitting a standard VECM into its component equations does not change the essence much. I suspect the ARDL model for cointegration has some differences from considering one equation of the regular VECM, doesn't it? So once again, what are the differences (besides ARDL having only one equation while VECM having multiple equations)? Also, is your question somehow specific due to the cointegration setting, or is it just about selecting the optimal number of lags for $\Delta y$s, $\Delta x_1$s and $\Delta x_2$s just as if they were variables of any other model? – Richard Hardy Oct 28 '15 at 20:18
• Also, when you say I find it hard to determine an optimal lag length for this model, do you mean the optimal lag lengths as there are three of them? – Richard Hardy Oct 28 '15 at 20:22
• @RichardHardy, because the VECM variables have equal lag orders, in other words, the lag order is fixed and the same for all differenced terms, it is easy to determine their length using an info criterion. With ARDL approach to cointegration, the differenced terms $\Delta x$'s are allowed to have different lag lengths. Moreover, in VECM you can have several error correction terms in each equation, whilst in ARDL you can have only one. ARDL approach allows the I(0), I(1) or fractionally integrated series to be included in the model. – mr.rox Oct 28 '15 at 20:41