What is an ARMA model and what is its general equation?

Conditions

• Time-series modeling
• Includes both lagged observations and lagged errors

Reasoning, step by step

1. Identify the AR component: $\phi_1 Y_{t-1} + \cdots + \phi_p Y_{t-p}$.
2. Identify the MA component: $\theta_1 e_{t-1} + \cdots + \theta_q e_{t-q}$.
3. Combine them with the intercept $\omega$ and current error $e_t$ into one equation.

Example

The slide title is 'Autoregressive Moving Average Models (ARMA)' and the text says 'Have both AR and MA terms together in the model.' The equation displayed is $Y_t = \omega + \phi_1 Y_{t-1} + \cdots + \phi_p Y_{t-p} + \theta_1 e_{t-1} + \cdots + \theta_q e_{t-q} + e_t$.

Common misconceptions

• Thinking ARMA models are just large AR or large MA models.
• Believing that ARMA models do not include an error term.

Watch the explanation

Explore next

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