help arima dialog: arima
also see: arima postestimation
-------------------------------------------------------------------------------
Title
[TS] arima -- ARIMA, ARMAX, and other dynamic regression models
Syntax
Basic syntax for a regression model with ARMA disturbances
arima depvar [indepvars], ar(numlist) ma(numlist)
Basic syntax for an ARIMA(p,d,q) model
arima depvar, arima(#p,#d,#q)
Basic syntax for a multiplicative seasonal ARIMA(p,d,q)*(P,D,Q)s model
arima depvar, arima(#p,#d,#q) sarima(#P,#D,#Q,#s)
Full syntax
arima depvar [indepvars] [if] [in] [weight] [, options]
options description
-------------------------------------------------------------------------
Model
noconstant suppress constant term
arima(#p,#d,#q) specify ARIMA(p,d,q) model for dependent
variable
ar(numlist) autoregressive terms of the structural
model disturbance
ma(numlist) moving-average terms of the structural
model disturbance
constraints(constraints) apply specified linear constraints
collinear keep collinear variables
Model 2
sarima(#P,#D,#Q,#s) specify period-#s multiplicative seasonal
ARIMA term
mar(numlist, #s) multiplicative seasonal autoregressive
terms; may be repeated
mma(numlist, #s) multiplicative seasonal moving-average
terms; may be repeated
Model 3
condition use conditional MLE instead of full MLE
savespace conserve memory during estimation
diffuse use diffuse prior for starting Kalman
filter recursions
p0(#|matname) use alternate prior for starting Kalman
recursions; seldom used
state(#|matname) use alternate state vector for starting
Kalman filter recursions
SE/Robust
vce(vcetype) vcetype may be opg, robust, or oim
Reporting
level(#) set confidence level; default is level(95)
detail report list of gaps in time series
nocnsreport do not display constraints
display_options control spacing
Maximization
maximize_options control the maximization process; seldom
used
+ coeflegend display coefficients' legend instead of
coefficient table
-------------------------------------------------------------------------
+ coeflegend does not appear in the dialog box.
You must tsset your data before using arima; see [TS] tsset.
depvar and indepvars may contain time-series operators; see tsvarlist.
by, rolling, statsby, and xi are allowed; see prefix.
iweights are allowed; see weights.
See [TS] arima postestimation for features available after estimation.
Menu
Statistics > Time series > ARIMA and ARMAX models
Description
arima fits univariate models with time-dependent disturbances. arima
fits a model of depvar on indepvars where the disturbances are allowed to
follow a linear autoregressive moving-average (ARMA) specification. The
dependent and independent variables may be differenced or seasonally
differenced to any degree. When independent variables are included in
the specification, such models are often called ARMAX models; and when
independent variables are not specified, they reduce to Box-Jenkins
autoregressive integrated moving-average (ARIMA) models in the dependent
variable. Multiplicative seasonal ARIMA and ARMAX models can also be
fit. Missing data are allowed and are handled using the Kalman filter
and methods outlined in [TS] arima.
In the full syntax, depvar is the variable being modeled, and the
structural or regression part of the model is specified in indepvars.
ar() and ma() specify the lags of autoregressive and moving-average
terms, respectively; and mar() and mma() specify the multiplicative
seasonal autoregressive and moving-average terms, respectively.
arima allows time-series operators in the dependent variable and
independent variable lists, and making extensive use of these operators
is often convenient; see tsvarlist for a discussion of time-series
operators.
arima typed without arguments redisplays the previous estimates.
Options
+-------+
----+ Model +------------------------------------------------------------
noconstant; see [R] estimation options.
arima(#p,#d,#q) is an alternative, shorthand notation for specifying
models with ARMA disturbances. The dependent variable and any
independent variables are differenced #d times, 1 through #p lags of
autocorrelations and 1 through #q lags of moving averages are
included in the model. For example, the specification
. arima D.y, ar(1/2) ma(1/3)
is equivalent to
. arima y, arima(2,1,3)
The latter is easier to write for simple ARMAX and ARIMA models, but
if gaps in the AR or MA lags are to be modeled, of if different
operators are to be applied to independent variables, the first
syntax is required.
ar(numlist) specifies the autoregressive terms of the structural model
disturbance to be included in the model. For example, ar(1/3)
specifies that lags of 1, 2, and 3 of the structural disturbance be
included in the model; ar(1 4) specifies that lags 1 and 4 be
included, perhaps to account for additive quarterly effects.
If the model does not contain regressors, these terms can also be
considered autoregressive terms for the dependent variable.
ma(numlist) specifies the moving-average terms to be included in the
model. These are the terms for the lagged innovations (white-noise
disturbances).
constraints(constraints), collinear; see [R] estimation options.
If constraints are placed between structural model parameters and
ARMA terms, the first few iterations may attempt steps into
nonstationary areas. This process can be ignored if the final
solution is well within the bounds of stationary solutions.
+---------+
----+ Model 2 +----------------------------------------------------------
sarima(#P,#D,#Q,#s) is an alternative, shorthand notation for specifying
the multiplicative seasonal components of models with ARMA
disturbances. The dependent variable and any independent variables
are lag-#s seasonally differenced #D times, and 1 through #P seasonal
lags of autoregressive terms and 1 through #Q seasonal lags of
moving-average terms are included in the model. For example, the
specification
. arima DS12.y, ar(1/2) mar(1/2,12) mma(1/2,12)
is equivalent to
. arima y, arima(2,1,3) sarima(2,1,2,12)
mar(numlist, #s) specifies the lag-#s multiplicative seasonal
autoregressive terms. For example, mar(1/2,12) requests that the
first two lag-12 multiplicative seasonal autoregressive terms be
included in the model.
mma(numlist, #s) specifies the lag-#s multiplicative seasonal
moving-average terms. For example, mma(1 3,12) requests that the
first and third (but not the second) lag-12 multiplicative seasonal
moving-average terms be included in the model.
+---------+
----+ Model 3 +----------------------------------------------------------
condition specifies that conditional, rather than full, maximum
likelihood estimates be produced. This estimation method is not
appropriate for nonstationary series but may be preferable for long
series or for models that have one or more long AR or MA lags.
diffuse, p0(), and state0() may not be specified with condition. See
[TS] arima for details.
savespace specifies that memory use be conserved by retaining only those
variables required for estimation. The original dataset is restored
after estimation. This option is rarely used and should be used only
if there is not enough space to fit a model without the option.
However, arima requires considerably more temporary storage during
estimation than most estimation commands in Stata.
diffuse specifies that a diffuse prior be used as a starting point for
the Kalman filter recursions. Using diffuse, nonstationary models
may be fit with arima (see the p0() option below; diffuse is
equivalent to specifying p0(1e9)). See [TS] arima for details.
p0(#|matname) is a rarely specified option that can be used for
nonstationary series or when an alternate prior for starting the
Kalman recursions is desired; see [TS] arima for details.
state0(#|matname) is a rarely used option that specifies an alternate
initial state vector for starting the Kalman filter recursions. If #
is specified, all elements of the vector are taken to be #. The
default initial state vector is state0(0).
+-----------+
----+ SE/Robust +--------------------------------------------------------
vce(vcetype) specifies the type of standard error reported, which
includes types that are robust to some kinds of misspecification and
that are derived from asymptotic theory; see [R] vce_option.
For state-space models in general and ARMAX and ARIMA models in
particular, the robust or quasi-maximum likelihood estimates (QMLEs)
of variance are robust to symmetric nonnormality in the disturbances,
including, as a special case, heteroskedasticity. The robust
variance estimates are not generally robust to functional
misspecification of the structural or ARMA components of the model.
+-----------+
----+ Reporting +--------------------------------------------------------
level(#); see [R] estimation options.
detail specifies that a detailed list of any gaps in the series be
reported, including gaps due to missing observations or missing data
for the dependent variable or independent variables.
nocnsreport; see [R] estimation options.
display_options: vsquish; see [R] estimation options.
+--------------+
----+ Maximization +-----------------------------------------------------
maximize_options: difficult, technique(algorithm_spec), iterate(#),
[no]log, trace, gradient, showstep, hessian, showtolerance,
tolerance(#), ltolerance(#), nrtolerance(#), gtolerance(#),
nonrtolerance(#), from(init_specs); see [R] maximize for all options
except gtolerance(), and see below for information on gtolerance().
These options are sometimes more important for ARIMA models than most
maximum likelihood models because of potential convergence problems
with ARIMA models, particularly if the specified model and the sample
data imply a nonstationary model.
Several alternate optimization methods, such as
Berndt-Hall-Hall-Hausman (BHHH) and Broyden-Fletcher-Goldfarb-Shanno
(BFGS), are provided for ARIMA models. Although ARIMA models are not
as difficult to optimize as ARCH models, their likelihoods are
nevertheless generally not quadratic and often pose optimization
difficulties; this is particularly true if a model is nonstationary
or nearly nonstationary. Because each method approaches optimization
differently, some problems can be successfully optimized by an
alternate method when one method fails.
Setting technique() to something other than the default or BHHH
changes the vcetype to vce(oim).
The following options are all related to maximization and are
particularly important in fitting ARIMA models.
technique(algorithm_spec) specifies the optimization technique to use
to maximize the likelihood function.
technique(bhhh) specifies the Berndt-Hall-Hall-Hausman (BHHH)
algorithm.
technique(dfp) specifies the Davidon-Fletcher-Powell (DFP)
algorithm.
technique(bfgs) specifies the Broyden-Fletcher-Goldfarb-Shanno
(BFGS) algorithm.
technique(nr) specifies Stata's modified Newton-Raphson (NR)
algorithm.
You can specify multiple optimization methods. For example,
technique(bhhh 10 nr 20)
requests that the optimizer perform 10 BHHH iterations, switch to
Newton-Raphson for 20 iterations, switch back to BHHH for 10 more
iterations, and so on.
The default for arima is technique(bhhh 5 bfgs 10).
gtolerance(#) specifies the tolerance for the gradient relative to
the coefficients. When |g_i*b_i| < gtolerance() for all
parameters b_i and the corresponding elements of the gradient
g_i, the gradient tolerance criterion is met. The default
gradient tolerance for arima is gtolerance(.05).
gtolerance(999) may be specified to disable the gradient
criterion. If the optimizer becomes stuck with repeated "(backed
up)" messages, the gradient probably still contains substantial
values, but an uphill direction cannot be found for the
likelihood. With this option, results can often be obtained, but
whether the global maximum likelihood has been found is unclear.
When the maximization is not going well, it is possible to set
the maximum number of iterations (see [R] maximize) to the point
where the optimizer appears to be stuck and to inspect the
estimation results at that point.
from(init_specs) specifies the starting values of the model
coefficients; see [R] maximize for a general discussion and
syntax options.
The standard syntax for from() accepts a matrix, a list of
values, or coefficient name value pairs; see [R] maximize. arima
also accepts from(armab0), which sets the starting value for all
ARMA parameters in the model to 0 prior to optimization.
ARIMA models may be sensitive to initial conditions and may have
coefficent values that correspond to local maximums. The default
starting values for arima are generally good, particularly in
large samples for stationary series.
The following option is available with arima but is not shown in the
dialog box:
coeflegend; see [R] estimation options.
Examples
---------------------------------------------------------------------------
Setup
. webuse wpi1
Simple ARIMA model with differencing and autoregressive and
moving-average components
. arima wpi, arima(1,1,1)
Same as above
. arima D.wpi, ar(1) ma(1)
ARIMA model with additive seasonal effects
. arima D.wpi, ar(1) ma(1 4)
---------------------------------------------------------------------------
Setup
. webuse air2
. generate lnair = ln(air)
Multiplicative SARIMA model
. arima lnair, arima(0,1,1) sarima(0,1,1,12) noconstant
---------------------------------------------------------------------------
Setup
. webuse friedman2, clear
ARMAX model
. arima consump m2 if tin(, 1981q4), ar(1) ma(1)
ARMAX model with robust standard errors
. arima consump m2 if tin(, 1981q4), ar(1) ma(1) vce(robust)
---------------------------------------------------------------------------
Saved results
arima saves the following in e():
Scalars
e(N) number of observations
e(N_gaps) number of gaps
e(k) number of parameters
e(k_eq) number of equations in e(b)
e(k_eq_model) number of equations in model Wald test
e(k_dv) number of dependent variables
e(k1) number of variables in first equation
e(df_m) model degrees of freedom
e(ll) log likelihood
e(sigma) sigma
e(chi2) chi-squared statistic
e(p) significance
e(tmin) minimum time
e(tmax) maximum time
e(ar_max) maximum AR lag
e(ma_max) maximum MA lag
e(rank) rank of e(V)
e(ic) number of iterations
e(rc) return code
e(converged) 1 if converged, 0 otherwise
Macros
e(cmd) arima
e(cmdline) command as typed
e(depvar) name of dependent variable
e(covariates) list of covariates
e(eqnames) names of equations
e(wtype) weight type
e(wexp) weight expression
e(title) title in estimation output
e(tmins) formatted minimum time
e(tmaxs) formatted maximum time
e(chi2type) Wald; type of model chi-squared test
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
e(ma) lags for moving-average terms
e(ar) lags for autoregressive terms
e(mari) multiplicative AR terms and lag i=1... (# seasonal
AR terms)
e(mmai) multiplicative MA terms and lag i=1... (# seasonal
AR terms)
e(seasons) seasonal lags in model
e(unsta) unstationary or blank
e(opt) type of optimization
e(ml_method) type of ml method
e(user) name of likelihood-evaluator program
e(technique) maximization technique
e(tech_steps) number of iterations performed before switching
techniques
e(crittype) optimization criterion
e(properties) b V
e(estat_cmd) program used to implement estat
e(predict) program used to implement predict
e(marginsok) predictions allowed by margins
e(marginsnotok) predictions disallowed by margins
Matrices
e(b) coefficient vector
e(Cns) constraints matrix
e(ilog) iteration log (up to 20 iterations)
e(gradient) gradient vector
e(V) variance-covariance matrix of the estimators
e(V_modelbased) model-based variance
Functions
e(sample) marks estimation sample
Also see
Manual: [TS] arima
Help: [TS] arima postestimation;
[TS] tsset, [TS] arch, [TS] dfactor, [TS] dvech, [TS] prais,
[TS] sspace, [R] regress
