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The general linear model for a time series *y _{t}* is

$${y}_{t}=\mu +{\epsilon}_{t}+{\displaystyle \sum _{i=1}^{\infty}{\psi}_{i}{\epsilon}_{t-i}=\mu +\psi (L){\epsilon}_{t},}$$ | (1) |

The coefficients $${\psi}_{i}$$ are sometimes called *dynamic multipliers*
[1]. You can interpret the coefficient $${\psi}_{j}$$ as the change in *y*_{t+j} due to a one-unit change in *ε _{t}*,

$$\frac{\partial {y}_{t+j}}{\partial {\epsilon}_{t}}={\psi}_{j}.$$

Provided the series $$\left\{{\psi}_{i}\right\}$$ is absolutely summable, Equation 1 corresponds to a stationary stochastic process [2]. For a stationary stochastic process, the impact on the process due to a change in *ε _{t}* is not permanent, and the effect of the impulse decays to zero. If the series $$\left\{{\psi}_{i}\right\}$$ is explosive, the process

The series $$\left\{{\psi}_{i}\right\}$$ describes the change in future values *y*_{t+i} due to a one-unit impulse in the innovation *ε _{t}*, with no other changes to future innovations $${\epsilon}_{t+1},{\epsilon}_{t+2},\dots $$. As a result, $$\left\{{\psi}_{i}\right\}$$ is often called the

[1] Hamilton, J. D. *Time Series Analysis*. Princeton, NJ: Princeton University Press, 1994.

[2] Wold, H. *A Study in the Analysis of Stationary Time Series*. Uppsala, Sweden: Almqvist & Wiksell, 1938.