## Stata 15 help for arima_postestimation

```
[TS] arima postestimation -- Postestimation tools for arima

Postestimation commands

The following postestimation commands are of special interest after
arima:

Command            Description
-------------------------------------------------------------------------
estat acplot       estimate autocorrelations and autocovariances
estat aroots       check stability condition of estimates
irf                create and analyze IRFs
psdensity          estimate the spectral density
-------------------------------------------------------------------------

The following standard postestimation commands are also available:

Command            Description
-------------------------------------------------------------------------
estat ic           Akaike's and Schwarz's Bayesian information criteria
(AIC and BIC)
estat summarize    summary statistics for the estimation sample
estat vce          variance-covariance matrix of the estimators (VCE)
forecast           dynamic forecasts and simulations
lincom             point estimates, standard errors, testing, and
inference for linear combinations of coefficients
lrtest             likelihood-ratio test
margins            marginal means, predictive margins, marginal effects,
and average marginal effects
marginsplot        graph the results from margins (profile plots,
interaction plots, etc.)
nlcom              point estimates, standard errors, testing, and
inference for nonlinear combinations of coefficients
predict            predictions, residuals, influence statistics, and
other diagnostic measures
predictnl          point estimates, standard errors, testing, and
inference for generalized predictions
test               Wald tests of simple and composite linear hypotheses
testnl             Wald tests of nonlinear hypotheses
-------------------------------------------------------------------------

Syntax for predict

predict [type] newvar [if] [in] [, statistic options]

statistic          Description
-------------------------------------------------------------------------
Main
xb                 predicted values for mean equation -- the differenced
series; the default
stdp               standard error of the linear prediction
y                  predicted values for the mean equation in y -- the
undifferenced series
mse                mean squared error of the predicted values
residuals          residuals or predicted innovations
yresiduals         residuals or predicted innovations in y, reversing any
time-series operators
-------------------------------------------------------------------------
These statistics are available both in and out of sample; type predict
... if e(sample) ... if wanted only for the estimation sample.
Predictions are not available for conditional ARIMA models fit to panel
data.

options                     Description
-------------------------------------------------------------------------
Options
dynamic(time_constant)    how to handle lags of y_t
t0(time_constant)         set starting point for the recursions to
time_constant
structural                calculate considering the structural
component only
-------------------------------------------------------------------------
time_constant is a # or a time literal, such as td(1jan1995) or
tq(1995q1); see Conveniently typing SIF values in [D] datetime.

Statistics > Postestimation

Description for predict

predict creates a new variable containing predictions such as expected
values and mean squared errors.  All predictions are available as static
one-step-ahead predictions or as dynamic multistep predictions, and you
can control when dynamic predictions begin.

Options for predict

+------+
----+ Main +-------------------------------------------------------------

xb, the default, calculates the predictions from the model.  If D.depvar
is the dependent variable, these predictions are of D.depvar and not
of depvar itself.

stdp calculates the standard error of the linear prediction xb.  stdp
does not include the variation arising from the disturbance equation;
use mse to calculate standard errors and confidence bands around the
predicted values.

y specifies that predictions of depvar be made, even if the model was
specified in terms of, say, D.depvar.

mse calculates the MSE of the predictions.

residuals calculates the residuals.  If no other options are specified,
these are the predicted innovations; that is, they include the ARMA
component.  If structural is specified, these are the residuals from
the structural equation; see structural below.

yresiduals calculates the residuals in terms of depvar, even if the model
was specified in terms of, say, D.depvar.  As with residuals, the
yresiduals are computed from the model, including any ARMA component.
If structural is specified, any ARMA component is ignored, and
yresiduals are the residuals from the structural equation; see
structural below.

+---------+
----+ Options +----------------------------------------------------------

dynamic(time_constant) specifies how lags of y_t in the model are to be
handled.  If dynamic() is not specified, actual values are used
everywhere that lagged values of y_t appear in the model to produce

dynamic(time_constant) produces dynamic (also known as recursive)
forecasts.  time_constant specifies when the forecast is to switch
from one step ahead to dynamic.  In dynamic forecasts, references to
y_t evaluate to the prediction of y_t for all periods at or after
time_constant; they evaluate to the actual value of y_t for all prior
periods.

For example, dynamic(10) would calculate predictions in which any
reference to y_t with t < 10 evaluates to the actual value of y_t and
any reference of y_t with t>10 evaluates to the prediction of y_t.
This means that one-step-ahead predictions are calculated for t < 10
and dynamic predictions thereafter.  Depending on the lag structure
of the model, the dynamic predictions might still refer to some
actual values of y_t.

You may also specify dynamic(.) to have predict automatically switch
from one-step-ahead to dynamic predictions at p + q, where p is the
maximum AR lag and q is the maximum MA lag.

t0(time_constant) specifies the starting point for the recursions to
compute the predicted statistics; disturbances are assumed to be 0
for t < t0().  The default is to set t0() to the minimum t observed
in the estimation sample, meaning that observations before that are
assumed to have disturbances of 0.

t0() is irrelevant if structural is specified because then all
observations are assumed to have disturbances of 0.

t0(5) would begin recursions at t=5.  If the data were quarterly, you
might instead type t0(tq(1961q2)) to obtain the same result.

The ARMA component of ARIMA models is recursive and depends on the
starting point of the predictions.  This includes one-step-ahead
predictions.

structural specifies that the calculation be made considering the
structural component only, ignoring the ARMA terms, producing the

Syntax for margins

margins [marginlist] [, options]

margins [marginlist] , predict(statistic ...) [predict(statistic ...)
...] [options]

statistic          Description
-------------------------------------------------------------------------
xb                 predicted values for mean equation -- the differenced
series; the default
y                  predicted values for the mean equation in y -- the
undifferenced series
stdp               not allowed with margins
mse                not allowed with margins
residuals          not allowed with margins
yresiduals         not allowed with margins
-------------------------------------------------------------------------

Statistics not allowed with margins are functions of stochastic
quantities other than e(b).

For the full syntax, see [R] margins.

Statistics > Postestimation

Description for margins

margins estimates margins of response for expected values.

Examples

Setup
. webuse wpi1

Fit ARIMA model with additive seasonal effects
. arima D.ln_wpi, ar(1) ma(1 4)

Compute predictions for D.ln_wpi
. predict xb

Consider structural component only -- ignore ARMA terms -- when making
predictions
. predict xbs, structural

Compute predictions for ln_wpi, reversing any time-series operators
applied in estimation
. predict y, y

Compute predictions for ln_wpi, using lagged forecasted values for
predictions after 1970q1 instead of lagged actual values
. predict yd, y dynamic(tq(1970q1))

Graph time-series line plot
. tsline y yd

```