Classical✓ Mathematical
◆ The PatternModeling dependence through past shocks
An MA(q) model expresses each value as a weighted sum of q past error terms. While AR uses past values, MA uses past surprises. ACF cutoff at lag q identifies the order.
yt = c + εt + θ1εt−1 + θ2εt−2 + … + θqεt−q
Each θ coefficient controls the impact of a past shock. MA models have finite memory — the effect of a shock dies out after exactly q steps.
// Interactive — MA(q) impulse response
θ10.60
Order (q)1
# Python — fit MA model from statsmodels.tsa.arima.model import ARIMA model = ARIMA(series, order=(0, 0, 2)).fit() # MA(2) print(model.summary())
Pattern bridge: MA models capture how surprises propagate — the same mechanism behind market overreaction. The finite memory of MA is the opposite of the persistent memory in AR models.