Moving-Average Models

What are moving‐average (MA) models?

Answer

Moving‐average models are (conceptually) linear regression models in time‐series analysis in which the predictors are the past white‐noise terms. An MA( $$q$$ ) model can be written as

y_t \;=\; \varepsilon_t \;+\; \theta_1\,\varepsilon_{t-1} \;+\; \theta_2\,\varepsilon_{t-2} \;+\;\dots+\; \theta_q\,\varepsilon_{t-q},

where $\{\varepsilon_t\}$ is white noise (zero mean, constant variance). Here, “MA( $$q$$ )” indicates there are $$q$$ lagged‐noise predictors ( $\varepsilon_{t-1},\dots,\varepsilon_{t-q}$ ) with coefficients $\theta_1,\dots,\theta_q$ .