# impulse

Generate regression model with ARIMA errors impulse response function

## Description

`impulse(`

plots a discrete stem plot of the
impulse response function (IRF)
for the regression model with ARIMA time series errors, `Mdl`

)`Mdl`

, in the
current figure window.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

To improve performance of the filtering algorithm, specify the number of observations,

`numObs`

, to include in the impulse response.

## Algorithms

If you specify the number of periods

`numObs`

,`impulse`

computes the IRF by filtering a unit shock followed by an appropriate length vector of zeros. The filtering algorithm is very fast and results in an IRF of`numObs`

length.If you do not specify

`numObs`

,`impulse`

implements this procedure:Convert the error model to a pure moving average (MA) polynomial by using the relatively slow lag operator polynomial division algorithm.

Truncate the pure MA polynomial according to default tolerances because the polynomial is generally of infinite degree.

This procedure produces an IRF of generally unknown length. For more details, see

`LagOp`

and`mldivide`

.

## 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.

## Version History

**Introduced in R2013b**