Static Model

A static model in time series is one where $x$ affects $y$ only contemporaneously: $y_t = \beta_0 + \beta_1 x_t + u_t$. There is no carry-over, no lags. It is the simplest time-series specification and assumes the entire impact of $x$ on $y$ happens in the same period.

When to use

Static models work when the relationship is genuinely immediate (e.g. today's weather → today's pollution dispersion, abstracting from yesterday's residual air mass). For most economic relationships — investment responding to interest rates, inflation responding to money supply — the immediate-effect assumption is too strong and a Distributed Lag Model or Autoregressive Model is more realistic.