summarize

Display ARIMA model estimation results

expand all in page

Syntax

summarize(Mdl)
results = summarize(Mdl)

Description

example

summarize(Mdl) displays a summary of the ARIMA model Mdl.

  • If Mdl is an estimated model returned by estimate, then summarize 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 by arima, then summarize prints the standard object display (the same display that arima prints during model creation).

example

results = summarize(Mdl) returns one of the following variables and does not print to the Command Window.

  • If Mdl is an estimated model, then results is a structure containing estimation results.

  • If Mdl is an unestimated model, then results is an arima model object that is equal to Mdl.

Input Arguments

expand all

ARIMA model, specified as an arima model object returned by estimate or arima.

Output Arguments

expand all

Model summary, returned as a structure array or an arima model object.

  • If Mdl is an estimated model, then results is a structure array containing the fields in this table.

    FieldDescription
    DescriptionModel summary description (string)
    SampleSizeEffective sample size (numeric scalar)
    NumEstimatedParametersNumber of estimated parameters (numeric scalar)
    LogLikelihoodOptimized loglikelihood value (numeric scalar)
    AICAkaike Information Criterion (numeric scalar)
    BICBayesian Information Criterion (numeric scalar)
    TableMaximum 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, then VarianceTable is a table containing one row.

    If Mdl.Variance is an estimated conditional variance model (for example, a garch model), then VarianceTable is a table whose rows correspond to estimated variance model parameters.

  • If Mdl is an unestimated model, then results is an arima model object that is equal to Mdl.

Examples

expand all

Open Live Script

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
Open Live Script

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

rt=c+ϕ1rt-1+εt,

where εt=σtzt,

σt2=κ+γ1σt-12+α1εt-12,

and zt 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      5.7086e-05
    AR{1}        0.13816      0.019893          6.945      3.7846e-12

 
 
    GARCH(1,1) Conditional Variance Model (Gaussian Distribution):
 
                 Value      StandardError    TStatistic      PValue  
                ________    _____________    __________    __________

    Constant    0.022377      0.0033201        6.7399      1.5852e-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      5.7086e-05
    AR{1}        0.13816      0.019893          6.945      3.7846e-12


varianceEstTbl = results.VarianceTable
varianceEstTbl=3×4 table
                 Value      StandardError    TStatistic      PValue  
                ________    _____________    __________    __________

    Constant    0.022377      0.0033201        6.7399      1.5852e-11
    GARCH{1}     0.87312      0.0091019        95.927               0
    ARCH{1}      0.11865       0.008717        13.611       3.434e-42

See Also

Objects

Functions

Introduced in R2018a

Econometrics Toolbox Documentation

Support