irf
Syntax
Description
irf
returns a numeric array representing the IRFs of the state and measurement variables in a state-space model. To plot the IRFs instead, use irfplot
. Other state-space model tools to characterize the dynamics of a specified system include:
The forecast error variance decomposition (FEVD), computed by
fevd
, provides information about the relative importance of each state disturbance in affecting the forecast error variance of all measurement variables in the system.Model-implied temporal correlations, computed by
corr
for a standard state-space model, measure the association between present and past state or measurement variables, as prescribed by the form of the model.
Fully Specified State-Space Model
uses additional options specified by one or more name-value pair arguments. For example, ResponseY
= irf(Mdl
,Name,Value
)'NumPeriods',10,'Cumulative',true
specifies a 10-period cumulative IRF starting at time 1, during which irf
applies the shock to a state-disturbance variable in the system, and ending at period 10.
Partially Specified State-Space Model and Confidence Interval Estimation
[
also returns, for each period, the lower and upper 95% Monte Carlo confidence bounds of each measurement variable IRF ([ResponseY
,ResponseX
,LowerY
,UpperY
,LowerX
,UpperX
] = irf(___,'Params'
,estParams,'EstParamCov'
,EstParamCov)LowerY
,UpperY
]) and each state variable IRF ([LowerX
,UpperX
]). EstParamCov
specifies the estimated covariance matrix of the parameter estimates, as returned by the estimate
function, and is required for confidence interval estimation.
Examples
Input Arguments
Output Arguments
More About
Algorithms
If you specify
'eigendecomposition'
for the'Method'
name-value pair argument,irf
attempts to diagonalize the state-transition matrix A by using the spectral decomposition.irf
resorts to recursive multiplication instead under at least one of these circumstances:An eigenvalue is complex.
The rank of the matrix of eigenvectors is less than the number of states
Mdl
is time varying.
irf
uses Monte Carlo simulation to compute confidence intervals.irf
randomly drawsNumPaths
variates from the asymptotic sampling distribution of the unknown parameters inMdl
, which is Np(Params
,EstParamCov
), where p is the number of unknown parameters.For each randomly drawn parameter set j,
irf
:Creates a state-space model that is equal to
Mdl
, but substitutes in parameter set jComputes the random IRF of the resulting model ψj(t), where t = 1 through
NumPaths
For each time t, the lower bound of the confidence interval is the
(1 –
quantile of the simulated IRF at period t ψ(t), wherec
)/2
=c
Confidence
. Similarly, the upper bound of the confidence interval at time t is the(1 –
upper quantile of ψ(t).c
)/2
Version History
Introduced in R2020b