\begin{definition}[Definition:Regression Model]
Let $S$ be a stochastic process based on an equispaced time series.
Let the values of $S$ at timestamps $t, t - 1, t - 2, \dotsc$ be $z_t, z_{t - 1}, z_{t - 2}, \dotsc$
Let $\tilde z_t, \tilde z_{t - 1}, \tilde z_{t - 2}, \dotsc$ be deviations from a constant mean level $\mu$:
:$\tilde z_t = z_t - \mu$
Let $M$ be a linear filter model defined as
:$\tilde z_t = \phi_1 \tilde x_1 + \phi_2 \tilde x_2 + \dotsb + \phi_p \tilde x_p + a$
which relates a dependent variable $z$ to a set of independent variables $x_1, x_2, \dotsc, x_p$ plus an error term $a$.
$M$ is known as a '''regression model'''.
\end{definition}