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An ARMA model combines autoregressive terms in past observations with moving-average terms in past errors within a single equation. The general equation is $Y_t = \omega + \phi_1 Y_{t-1} + \cdots + \phi_p Y_{t-p} + \theta_1 e_{t-1} + \cdots + \theta_q e_{t-q} + e_t$.

Conditions: Time-series modeling; Includes both lagged observations and lagged errors

An ARMA model combines autoregressive terms in past observations with moving-average terms in past errors within a single equation. The general equation is $Y_t = \omega + \phi_1 Y_{t-1} + \cdots + \phi_p Y_{t-p} + \theta_1 e_{t-1} + \cdots + \theta_q e_{t-q} + e_t$.

Conditions: Time-series modeling; Includes both lagged observations and lagged errors

AR models forecast a series based solely on past values of the series, called lags. MA models forecast a series based solely on past errors in the series, called error lags.

Conditions: Forecasting a time series; Uses past values of the same series for AR; Uses past errors for MA

AR models forecast a series based solely on past values of the series, called lags. MA models forecast a series based solely on past errors in the series, called error lags.

Conditions: Forecasting a time series; Uses past values of the same series for AR; Uses past errors for MA

AR models are called long memory models because one can recursively look back over time and still see effects from lags. The effect of earlier observations can be traced backward recursively through lagged dependence.

Conditions: Applies to autoregressive time-series models; Assumes recursive substitution backward in time

AR models are called long memory models because one can recursively look back over time and still see effects from lags. The effect of earlier observations can be traced backward recursively through lagged dependence.

Conditions: Applies to autoregressive time-series models; Assumes recursive substitution backward in time