State-space models
Stata’s sspace command makes it easy to fit a wide variety
of multivariate time-series models by casting them as linear state-space
models, including vector autoregressive moving-average (VARMA) models,
structural time-series (STS) models, and dynamic-factor models.
State-space models parameterize the observed dependent variables as
functions of unobserved state variables. Stata’s state-space model
command, sspace, allows both the
observed dependent variables and the unobserved state variables to be
functions of exogenous covariates.
Stata’s state-space model command
sspace uses two forms of the Kalman filter to recursively obtain
conditional means and variances of both the unobserved states and the
measured dependent variables that are used to compute the likelihood
function. sspace allows you to specify your state-space model in
either the
covariance form or the error form. sspace works with state-space
models that are
nonstationary and models that are stationary. Options allow you to
specify the structures of the error covariance matrices for the state and
observation equations, and other options allow you to specify how the
initial values for the Kalman filter are obtained.
We have data on the natural log of the capacity utilization rate for the
manufacturing sector of the U.S. economy, lncaputil, and on the log of
manufacturing hours, lnhours. We treat these variables as
first-difference stationary, and we model D.lncaputil and
D.lnhours as a restricted first-order vector autoregressive
moving-average (VARMA(1,1)) process.
We can obtain one-step predictions of the two unobserved states from the
state-space model by typing
. predict u1 u2, states
We can graph those predicted states by typing
. tsline u1 u2
We can obtain one-step predictions of our two dependent variables by typing
. predict caputilhat hourshat
A graph comparing the one-step predictions of the difference in the log of
capacity utilization with its predictions is created by typing
. tsline D.lncaputil caputilhat
View more time series capabilities.
Explore more about state-space models
in Stata.
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