Interpretation of largest inverse root in a stationary time series

Let’s consider a stationary time series that can be modelled with an AR(p). I know that the cumulative effect of a shock is given by$$ frac{1}{1- sum^p theta_i}, $$ where $theta$ are the coefficients of the lag polynomial.I was wondering if there was any interpretation ( excluding stationarity) for the biggest (inverse) root in case of a shock to the time series.