Moving average model

In a moving average model, past shocks impact the current value of the variable directly, rather than having an indirect iterated effect that flows through past values of the observed variable. Thus you can read off the impulse response of a shock directly from the moving average coefficients.

Notably, in a moving average model only the last q shocks affect the current value of the variable. This is in contrast to an autoregressive model where a shock impacts the variable forever.

As noted in Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments, the moving average model can be reached in a somewhat roundabout way by running a regression of the current value of the observed variable against current and past shocks:

Thus, a moving-average model is conceptually a linear regression of the current value of the series against current and previous (observed) white noise error terms or random shocks. (Wikipedia)


References

Moving-average model - Wikipedia

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