# Lag order selection in error correction model (ECM)

I am building an Error Correction Model for monthly price data ($X, Y, Z$). I am deliberately using an ECM and not VECM and apply a two step approach (estimating cointegration relationship first, then ECM using residuals $resid$).

My ECM equation basically is: $$\Delta X_t = \alpha + \sum_{i=1}^{k}\beta_t \Delta X_{t-i} + \sum_{i=0}^{l}\gamma_t \Delta Y_{t-i} + \sum_{i=0}^{m}\delta_t \Delta Z_{t-i} + \lambda resid_{t-1} + \varepsilon_t$$

What I am not quite sure about and have read different approaches for, is the best approach with which to select the appropriate number of lags for the ECM, that is the values for $k, l, m$

1. As I understand it $k=l=m$ is not required.
2. One approach I found is starting with for example 12 lags for all series (due to monthly nature of data) and then reducing the number of lags step wise to the first (as in "the highest") significant lag for each series.
3. This approach seems sensitive to the order in which I reduce the lags. So if for example I first reduce $m$ to $8$ it might seem like the highest significant lag for $l$ is $6$ where if I would have started on $l$ I might have come up with a different combination

Thanks for your thoughts on this topic.

• I have fixed the time subscripts in the equation (I hope I did not mess them up). I also included the feature-selection tag, it could attract more attention. I don't think your ECM is much different from VECM; the only difference I see is that you have only one equation rather than three. (I think that having different lag orders for different variables could be allowed in VECM as well as ECM. Also, VECM works in two steps as well with first estimating the coint. relationship and then running the regressions.) – Richard Hardy Mar 7 '16 at 10:02
• By the way, should you have contemporaneous $\Delta Y_t$ and $\Delta Z_t$ on the right hand side (as you do now)? That would make a difference from the VECM, but that would also cause some problem with endogeneity, wouldn't it? – Richard Hardy Mar 7 '16 at 10:22
• I have edited the formula further to actually represent what I mean. Thank you for your first edit. Indeed currently I am including $i=0$ for $\Delta Y_t$ and $\Delta Z_t$ (and obviously not for $\Delta X_t$). Should I not do so? – Low Mar 7 '16 at 14:07
• Yeah, now I see I had made a stupid mistake there in the time indices; you got it right this time. Regarding contemporaneous regressors, they normally cause trouble due to endogeneity which makes regression coefficients inconsistent. You may check a textbook or some established examples of error correction models to see whether you should have these terms there. – Richard Hardy Mar 7 '16 at 14:50