summarize
Display ARIMA model estimation results
Description
summarize(
displays a summary of the ARIMA model Mdl
)Mdl
.
If
Mdl
is an estimated model returned byestimate
, thensummarize
prints estimation results to the MATLAB® Command Window. The display includes an estimation summary and a table of parameter estimates with corresponding standard errors, t statistics, and p-values. The estimation summary includes fit statistics, such as the Akaike Information Criterion (AIC), and the estimated innovations variance.If
Mdl
is an unestimated model returned byarima
, thensummarize
prints the standard object display (the same display thatarima
prints during model creation).
Input Arguments
Output Arguments
results
— Model summary
structure array | arima
model object
Model summary, returned as a structure array or an arima
model object.
If
Mdl
is an estimated model, thenresults
is a structure array containing the fields in this table.Field Description Description
Model summary description (string) SampleSize
Effective sample size (numeric scalar) NumEstimatedParameters
Number of estimated parameters (numeric scalar) LogLikelihood
Optimized loglikelihood value (numeric scalar) AIC
Akaike Information Criterion (numeric scalar) BIC
Bayesian Information Criterion (numeric scalar) Table
Maximum likelihood estimates of the model parameters with corresponding standard errors, t statistics (estimate divided by standard error), and p-values (assuming normality); a table with rows corresponding to model parameters VarianceTable
Maximum likelihood estimate of the model variance with corresponding standard errors, t statistics (estimate divided by standard error), and p-values (assuming normality).
If
Mdl.Variance
is constant, thenVarianceTable
is a table containing one row.If
Mdl.Variance
is an estimated conditional variance model (for example, agarch
model), thenVarianceTable
is a table whose rows correspond to estimated variance model parameters.If
Mdl
is an unestimated model, thenresults
is anarima
model object that is equal toMdl
.
Examples
Display Estimation Results
Print the results from estimating an ARMA model using simulated data.
Simulate data from an ARMA(1,1) model using known parameter values.
MdlSim = arima('Constant',0.01,'AR',0.8,'MA',0.14,... 'Variance',0.1); rng 'default'; Y = simulate(MdlSim,100);
Fit an ARMA(1,1) model to the simulated data, turning off the print display.
Mdl = arima(1,0,1); EstMdl = estimate(Mdl,Y,'Display','off');
Print the estimation results.
summarize(EstMdl)
ARIMA(1,0,1) Model (Gaussian Distribution) Effective Sample Size: 100 Number of Estimated Parameters: 4 LogLikelihood: -41.296 AIC: 90.592 BIC: 101.013 Value StandardError TStatistic PValue ________ _____________ __________ __________ Constant 0.044537 0.046038 0.96741 0.33334 AR{1} 0.82289 0.071163 11.563 6.3104e-31 MA{1} 0.12032 0.10182 1.1817 0.23731 Variance 0.13373 0.017879 7.4794 7.466e-14
Extract Estimation Results from Fitting Composite Conditional Mean and Variance Model
Load the NASDAQ data included with Econometrics™ toolbox. Convert the daily close composite index series to a return series. For numerical stability, convert the returns to percentage returns. Specify an AR(1) and GARCH(1,1) composite model. This is a model of the form
where ,
and is an independent and identically distributed standardized Gaussian process.
load Data_EquityIdx nasdaq = DataTable.NASDAQ; r = 100*price2ret(nasdaq); T = length(r); Mdl = arima('ARLags',1,'Variance',garch(1,1));
Fit the model Mdl
to the return series r
by using estimate
. Use the presample observations that estimate
chooses by default.
EstMdl = estimate(Mdl,r,'Display','params');
ARIMA(1,0,0) Model (Gaussian Distribution): Value StandardError TStatistic PValue ________ _____________ __________ __________ Constant 0.072632 0.018047 4.0245 5.7087e-05 AR{1} 0.13816 0.019893 6.945 3.7847e-12 GARCH(1,1) Conditional Variance Model (Gaussian Distribution): Value StandardError TStatistic PValue ________ _____________ __________ __________ Constant 0.022377 0.0033201 6.7399 1.5851e-11 GARCH{1} 0.87312 0.0091019 95.927 0 ARCH{1} 0.11865 0.008717 13.611 3.434e-42
Create a variable named results
that contains the estimation results by using summarize
.
results = summarize(EstMdl)
results = struct with fields:
Description: "ARIMA(1,0,0) Model (Gaussian Distribution)"
SampleSize: 3027
NumEstimatedParameters: 5
LogLikelihood: -4.7414e+03
AIC: 9.4929e+03
BIC: 9.5230e+03
Table: [2x4 table]
VarianceTable: [3x4 table]
Extract the parameter estimate summary tables from the estimation results structure array by using dot notation. The Table
field contains the conditional mean model parameter estimates and inferences. The VarianceTable
field contains the conditional variance model parameter estimates and inferences.
meanEstTbl = results.Table
meanEstTbl=2×4 table
Value StandardError TStatistic PValue
________ _____________ __________ __________
Constant 0.072632 0.018047 4.0245 5.7087e-05
AR{1} 0.13816 0.019893 6.945 3.7847e-12
varianceEstTbl = results.VarianceTable
varianceEstTbl=3×4 table
Value StandardError TStatistic PValue
________ _____________ __________ __________
Constant 0.022377 0.0033201 6.7399 1.5851e-11
GARCH{1} 0.87312 0.0091019 95.927 0
ARCH{1} 0.11865 0.008717 13.611 3.434e-42
Version History
Introduced in R2018a
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