The AIC and SBIC criteria recommended a lag length of 2 for ADF testing CPI data. At this lag length, it is stationary after first differencing and this is I(1).
However, when estimating the full VECM, the SBIC and AIC recommend a lag length of 4, however when I ADF tested the CPI data with this lag length it was non stationary after first differencing, I(2). Should I run the VECM model with 4 lags anyway? Running it at 2 lags leads to autocorrelation. , will this impact the results in any way?