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Generate ARMA model impulse responses

`armairf(ar0,ma0)`

`armairf(ar0,ma0,Name,Value)`

`Y = armairf(ar0,ma0)`

`Y = armairf(ar0,ma0,Name,Value)`

`armairf(`

returns
a tiered plot of the impulse response function, or dynamic response
of the system, that results from applying a one standard deviation
shock to each of the `ar0`

,`ma0`

)`numVars`

time series variables
composing an ARMA(*p*,*q*) model.
The autoregressive and moving average coefficients of the ARMA(*p*,*q*)
model are `ar0`

and `ma0`

, respectively.

The `armairf`

function

Accepts:

Vectors or cell vectors of matrices in difference-equation notation.

`LagOp`

lag operator polynomials corresponding to the AR and MA polynomials in lag operator notation.

Accommodates time series models that are univariate or multivariate, stationary or integrated, structural or in reduced form, and invertible or noninvertible.

Assumes that the model constant

*c*is 0.

`armairf(`

returns
a tiered plot of the impulse response function with additional options
specified by one or more `ar0`

,`ma0`

,`Name,Value`

)`Name,Value`

pair arguments.
For example, you can specify the number of periods to plot the impulse
response function or the computation method to use.

returns
the impulse responses with additional options specified by one or
more `Y`

= armairf(`ar0`

,`ma0`

,`Name,Value`

)`Name,Value`

pair arguments.

To compute

*forecast error impulse responses*, use the default value of`InnovCov`

, which is a`numVar`

-by-`numVars`

identity matrix. In this case, all available computation methods (see`Method`

) result in equivalent impulse response functions.To accommodate structural ARMA(

*p*,*q*) models, specify the input arguments`ar0`

and`ma0`

as`LagOp`

lag operator polynomials.

If

`Method`

is`'orthogonalized'`

, then the resulting impulse response function depends on the order of the variables in the time series model. If`Method`

is`'generalized'`

, then the resulting impulse response function is invariant to the order of the variables. Therefore, the two methods generally produce different results.If

`InnovCov`

is a diagonal matrix, then the resulting generalized and orthogonal impulse response functions are identical. Otherwise, the resulting generalized and orthogonal impulse response functions are identical when the first variable shocks all variables only (in other words,`Y(:,:,1)`

).

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

[2] Lutkepohl, H. *New Introduction
to Multiple Time Series Analysis.* Springer-Verlag, 2007.

[3] Pesaran, H. H. and Y. Shin. “Generalized Impulse
Response Analysis in Linear Multivariate Models.” *Economic
Letters.* Vol. 58, 1998, 17–29.

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