Seasonal Average Model

Definition

A model for seasonal trends with period $p$ (e.g., $p=12$ for monthly data). $Z_t={\mu }_t+X_t,{\mu }_t={\mu }_{t+p}$

The mean ${\mu }_t$ is assumed to be constant within each “season”: ${\mu }_t={\beta }_i\text{ for }t\text{ in season }i$ where $i=1,\dots ,p$.

Basically, ${\mu }_t={\beta }_i$ is the constant of $i$-th season