Mistake: a small one-step error stays small

“The one-step error is 1%, so the twelve-step forecast is about 1% off.”

w, err = 1.1, 0.01
grown = err * w ** 12
shrunk = err * 0.9 ** 12
assert round(grown, 4) == 0.0314
assert grown > 3 * err
assert shrunk < err

At w = 1.1 the 1% error is over 3% after twelve steps; at w = 0.9 it dies away. A recursive forecast eats its own output, so the update rule is applied to the error as well.

The horizon error depends on the coefficients, not on the one-step error alone. At w = 1.0 it neither grows nor shrinks.