ARMA Models
What is an ARMA model?
Answer
ARMA is a time‐series model which is a combination of AR and MA, hence the name autoregressive moving average. It can be written as
\[
y_t = \underbrace{\phi_1 y_{t-1} + \dots + \phi_p y_{t-p}}_{\text{AR}(p)\,\text{part}}
\;+\;\varepsilon_t
\;+\;\underbrace{\theta_1 \varepsilon_{t-1} + \dots + \theta_q \varepsilon_{t-q}}_{\text{MA}(q)\,\text{part}},
\]
where \(\{\varepsilon_t\}\) is white noise.
The hyperparameters are:
\(p\): number of lagged values \(y_{t-1},\dots,y_{t-p}\) used as predictors.
\(q\): number of lagged white‐noise terms \(\varepsilon_{t-1},\dots,\varepsilon_{t-q}\) used as predictors.