Testing whether forecasting models differ significantly in their forecasts I am not finding my question on here which I sort of find it hard to believe unless I am simply on the wrong stack board. If it is on this board, kindly direct me and I will be grateful. Otherwise, I have two models used to forecasting the same data set. I want to find out if my models are producing significantly different forecasts or not. How would I go about doing this?
Null: Models do not differ.
Alt: Models do differ from one another.
Models are used to forecast demand.
 A: Comments are correct that this question is quite vague, somewhat
less so in view of your response. But I will try to give an answer
that shows various statistical procedures that may be useful.
Suppose you have 100 paired forecasts as in vectors x1 and x1 below;
How well do they agree?
We can look at descriptive statistics of their differences:
d = x2 - x1
summary(d); length(d);  sd(d)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.2626  1.3748  2.0057  1.9440  2.5832  5.0812 
[1] 100        # number of differences
[1] 0.9689753  # standard deviation

hist(d, prob=T, col="skyblue2")


So it appears that forecasts $X_2$ are mostly larger than
forecasts $X_1.$ However, the two forecasts are highly correlated,
so it may not make much difference which forecast is used.
cor(x1,x2)
[1] 0.9989661

plot(x1, x2);  abline(0, 1, col="green2")


Nevertheless, we do know that the forecasts are not exactly the same,
and we can do a formal test whether the two are significantly
different in a statistical sense. The histogram of differences
looks roughly normal, so we use a paired t test. The tiny P-value
very near $0$ shows that the two forecasts are significantly different.
t.test(x1, x2, pair=T)

       Paired t-test

data:  x1 and x2
t = -20.063, df = 99, p-value < 2.2e-16
alternative hypothesis: 
  true difference in means is not equal to 0
95 percent confidence interval:
 -2.136304 -1.751773
sample estimates:
mean of the differences 
              -1.944039 

A nonparametric Wilcoxon paired (signed rank) test also shows a hightly
significant difference with a P-value very near $0:$
wilcox.test(x1, x2, pair=T)$p.val
[1] 6.407145e-18

However, statistical significance is not the same thing as practical importance.
If the fact that $X_2$ forecasts average about $2$ higher then
$X_1$ forecasts is not important, and because the two never seem to be
far apart, then it may not make any practical difference which
forecast is used.
By contrast, if a difference of $2$ is of practical importance, we
should look at the record of past performance and use the forecasting
method that has been most often correct.

Note: The following R code was used to simulate x1 and x2:
set.seed(121)
x1 = rgamma(100, 5, .1)
x2 = x1 + rnorm(100, 2, 1)

