I am comparing the forecasting accuracy of a VAR estimated in levels and first differences. I am working in R, but my question is language agnostic (although if you have an answer with R code, that will be appreciated.)
Specifically, when estimating a VAR in levels, the forecast that you'll get from your statistical package will be in the levels of that variable. If you care about the future levels of a time series, that is great, you're done.
If you forecast in first-differences, the statistical package will likely provide you forecasts of future first-differences in the time series, not the levels. So my question is if I estimate a VAR in first-differences, is there any problem with just applying the forecasted first-differences iteratively with an initial value equal to the last observed data point in the time-series? Is this equivalent to taking the first-differenced VAR model (i.e. the coefficients) and applying it to the level data to obtain forecasted levels?
For R users, I'm asking if I can estimate a VAR in first differences, call it
var_fd, and pass it to the
forecast function, and then back out the forecasted levels using
diffinv and my last observed data point.