summarize

Display ARIMA model estimation results

Syntax

summarize(Mdl)

results = summarize(Mdl)

Description

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).

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

Mdl — ARIMA model

arima model object

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

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, then results 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, 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

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

$$r_t=c+{\varphi }_1{r}_{t-1}+{\epsilon }_t,$$

where $${\epsilon }_t={\sigma }_t{z}_t$$,

$${\sigma }_t^2=\kappa +{\gamma }_1{\sigma }_{t-1}^2+{\alpha }_1{\epsilon }_{t-1}^2,$$

and $$z_t$$ 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