Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Filter disturbances through vector error-correction (VEC) model

`Y = filter(Mdl,Z)`

`Y = filter(Mdl,Z,Name,Value)`

```
[Y,E] =
filter(___)
```

uses additional
options specified by one or more name-value pair arguments. For example, `Y`

= filter(`Mdl`

,`Z`

,`Name,Value`

)`'X',X,'Scale',false`

specifies
`X`

as exogenous predictor data for the regression component
and refraining from scaling the disturbances by the lower triangular Cholesky factor
of the model innovations covariance matrix.

`filter`

computes`Y`

and`E`

using this process for each pagein`j`

`Z`

.If

`Scale`

is`true`

, then`E(:,:,`

=)`j`

`L*Z(:,:,`

, where)`j`

`L`

=`chol(Mdl.Covariance,'lower')`

. Otherwise,`E(:,:,`

=)`j`

`Z(:,:,`

. Set)`j`

*e*=_{t}`E(:,:,`

.)`j`

`Y(:,:,`

is)`j`

*y*in this system of equations._{t}$$\Delta {y}_{t}={\widehat{\Phi}}^{-1}(L)\left(\widehat{c}+\widehat{d}t+\widehat{A}\widehat{B}\prime {y}_{t-1}+\widehat{\beta}{x}_{t}+{e}_{t}\right).$$

For variable definitions, see Vector Error-Correction Model.

`filter`

generalizes`simulate`

. Both functions filter a disturbance series through a model to produce responses and innovations. However, whereas`simulate`

generates a series of mean-zero, unit-variance, independent Gaussian disturbances`Z`

to form innovations`E`

=`L*Z`

,`filter`

enables you to supply disturbances from any distribution.`filter`

uses this process to determine the time origin*t*_{0}of models that include linear time trends.If you do not specify

`Y0`

, then*t*_{0}= 0.Otherwise,

`filter`

sets*t*_{0}to`size(Y0,1)`

–`Mdl.P`

. Therefore, the times in the trend component are*t*=*t*_{0}+ 1,*t*_{0}+ 2,...,*t*_{0}+`numobs`

, where`numobs`

is the effective sample size (`size(Y,1)`

after`filter`

removes missing values). This convention is consistent with the default behavior of model estimation in which`estimate`

removes the first`Mdl.P`

responses, reducing the effective sample size. Although`filter`

explicitly uses the first`Mdl.P`

presample responses in`Y0`

to initialize the model, the total number of observations in`Y0`

and`Y`

(excluding missing values) determines*t*_{0}.

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

[2]
Johansen, S. *Likelihood-Based Inference in Cointegrated Vector Autoregressive Models*. Oxford: Oxford University Press, 1995.

[3]
Juselius, K. *The Cointegrated VAR Model*. Oxford: Oxford University Press, 2006.

[4]
Lütkepohl, H. *New Introduction to Multiple Time Series Analysis*. Berlin: Springer, 2005.