filter
Filter disturbances through vector error-correction (VEC) model
Description
uses additional
options specified by one or more name-value 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.
Examples
Input Arguments
Output Arguments
Algorithms
filter
computesY
andE
using this process for each pagej
inZ
.If
Scale
istrue
, thenE(:,:,
=j
)L*Z(:,:,
, wherej
)L
=chol(Mdl.Covariance,'lower')
. Otherwise,E(:,:,
=j
)Z(:,:,
. Set et =j
)E(:,:,
.j
)Y(:,:,
is yt in this system of equations.j
)For variable definitions, see Vector Error-Correction Model.
filter
generalizessimulate
. Both functions filter a disturbance series through a model to produce responses and innovations. However, whereassimulate
generates a series of mean-zero, unit-variance, independent Gaussian disturbancesZ
to form innovationsE
=L*Z
,filter
enables you to supply disturbances from any distribution.filter
uses this process to determine the time origin t0 of models that include linear time trends.If you do not specify
Y0
, then t0 = 0.Otherwise,
filter
sets t0 tosize(Y0,1)
–Mdl.P
. Therefore, the times in the trend component are t = t0 + 1, t0 + 2,..., t0 +numobs
, wherenumobs
is the effective sample size (size(Y,1)
afterfilter
removes missing values). This convention is consistent with the default behavior of model estimation in whichestimate
removes the firstMdl.P
responses, reducing the effective sample size. Althoughfilter
explicitly uses the firstMdl.P
presample responses inY0
to initialize the model, the total number of observations inY0
andY
(excluding missing values) determines t0.
References
[1] Hamilton, James 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.