The general linear model for a time series yt is
where denotes the infinite-degree lag operator polynomial .
The coefficients are sometimes called dynamic multipliers . You can interpret the coefficient as the change in yt+j due to a one-unit change in εt,
Provided the series is absolutely summable, Equation 5-19 corresponds to a stationary stochastic process . For a stationary stochastic process, the impact on the process due to a change in εt is not permanent, and the effect of the impulse decays to zero. If the series is explosive, the process yt is nonstationary. In this case, a one-unit change in εt permanently affects the process.
The series describes the change in future values yt+i due to a one-unit impulse in the innovation εt, with no other changes to future innovations . As a result, is often called the impulse response function.
 Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
 Wold, H. A Study in the Analysis of Stationary Time Series. Uppsala, Sweden: Almqvist & Wiksell, 1938.