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Impulse Response Function

The general linear model for a time series y_t is

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,

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 y_t is nonstationary. In this case, a one-unit change in ε_t permanently affects 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 impulse response function.

See Also

armairf | impulse

Related Examples

• Plot the Impulse Response Function

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