simulate
Monte Carlo simulation of vector error-correction (VEC) model
Description
uses additional
options specified by one or more name-value arguments. For example, Y
= simulate(Mdl
,numobs
,Name,Value
)'NumPaths',1000,'X',X
specifies
simulating 1000 paths and X
as exogenous predictor data for the
regression component.
Examples
Input Arguments
Output Arguments
Algorithms
simulate
performs conditional simulation using this process for all pagesk
= 1,...,numpaths
and for each timet
= 1,...,numobs
.simulate
infers (or inverse filters) the innovationsE(
from the known future responsest
,:,k
)YF(
. Fort
,:,k
)E(
,t
,:,k
)simulate
mimics the pattern ofNaN
values that appears inYF(
.t
,:,k
)For the missing elements of
E(
,t
,:,k
)simulate
performs these steps.Draw
Z1
, the random, standard Gaussian distribution disturbances conditional on the known elements ofE(
.t
,:,k
)Scale
Z1
by the lower triangular Cholesky factor of the conditional covariance matrix. That is,Z2
=L*Z1
, whereL
=chol(C,'lower')
andC
is the covariance of the conditional Gaussian distribution.Impute
Z2
in place of the corresponding missing values inE(
.t
,:,k
)
For the missing values in
YF(
,t
,:,k
)simulate
filters the corresponding random innovations through the modelMdl
.
simulate
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,
simulate
sets t0 tosize(Y0,1)
–Mdl.P
. Therefore, the times in the trend component are t = t0 + 1, t0 + 2,..., t0 +numobs
. This convention is consistent with the default behavior of model estimation in whichestimate
removes the firstMdl.P
responses, reducing the effective sample size. Althoughsimulate
explicitly uses the firstMdl.P
presample responses inY0
to initialize the model, the total number of observations inY0
(excluding any 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.