On Mon, 2 Apr 2012, Daniel Bencik wrote:
I have two models for daily ranges prediction, one of them
being a pure VECM of high and low prices and the other one
being the same augmented by other variables. On in sample,
the first model has RSQ~20% for both variables, the second
has RSQ~55% both both. However, when I do rolling forecasts,
the forecasts end up being nearly the same, DMW test says
they are of the same quality. And this is surprising for
everybody I told.
Your script indicates that what you're actually forecasting is
the difference between two cointegrated variables. As in (with
simplified notation)
OOSMatrix[t] = $fcast[1] - $fcast[2]
where, in context, $fcast is a 2-vector containing the
one-step ahead forecasts for the two series at a given
observation.
Seems to me, it would not be very surprising if your bigger
model produced a better fit for the two series individually
(hence higher R-squared values) but the smaller model did just
about as well at forecasting their difference. They are
supposed to be cointegrated, after all.
Allin Cottrell