# impulse

Generate univariate ARIMA model impulse response function (IRF)

## Description

returns the impulse response function (IRF)
of the input univariate ARIMA model. `y`

= impulse(`Mdl`

)`impulse`

returns the dynamic
responses starting at period 0, during which `impulse`

applies a
unit shock to the innovation.

`impulse(___)`

plots a discrete stem plot of the IRF of
the input ARIMA model to the current axes, using any of the input argument combinations in
the previous syntaxes.

`impulse(`

plots on the axes specified by `ax`

,___)`ax`

instead of
the current axes (`gca`

). `ax`

can precede any of the input
argument combinations in the previous syntaxes.* (since R2024a)*

`[___,`

plots the IRF and additionally returns handles to the plotted graphics objects. Use elements of `h`

]
= impulse(___)`h`

to modify properties of the plot after you create it.* (since R2024a)*

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

To improve performance of the filtering algorithm, specify the number of periods to include in the IRF

`numObs`

. When you do not specify`numObs`

,`impulse`

computes the IRF by using the lag operator polynomial division algorithm, which is relatively slow, to represent the input model`Mdl`

as a truncated, infinite-degree, moving average model. The length of the resulting IRF is generally unknown.

## Alternative Functionality

The `armairf`

function generates or plots the IRF of an
ARMA process specified by input AR and MA lag operator polynomial coefficients.

## References

[1] Box, George E. P., Gwilym M. Jenkins, and Gregory C. Reinsel. *Time Series Analysis: Forecasting and Control*. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[2] Enders, Walter. *Applied Econometric Time Series*. Hoboken, NJ: John Wiley & Sons, Inc., 1995.

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

[4] Lütkepohl, Helmut. *New Introduction to Multiple Time Series Analysis*. New York, NY: Springer-Verlag, 2007.

[5] Wold, Herman. "A Study in the Analysis of Stationary Time
Series." *Journal of the Institute of Actuaries* 70 (March 1939): 113–115.
https://doi.org/10.1017/S0020268100011574.

## Version History

**Introduced in R2012a**