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Class: arima

Display parameter estimation results for ARIMA or ARIMAX models




print(EstMdl,EstParamCov) displays parameter estimates, standard errors, and t statistics for a fitted ARIMA or ARIMAX model.

Input Arguments


arima model estimated using estimate.


Estimation error variance-covariance matrix, as output by estimate. EstParamCov is a square matrix with a row and column for each parameter known to the optimizer when Mdl was fit by estimate. Known parameters include all parameters estimate estimated. If you specified a parameter as fixed during estimation, then it is also a known parameter and the rows and columns associated with it contain 0s.

The parameters in EstParamCov are ordered as follows:

  • Constant

  • Nonzero AR coefficients at positive lags

  • Nonzero SAR coefficients at positive lags

  • Nonzero MA coefficients at positive lags

  • Nonzero SMA coefficients at positive lags

  • Regression coefficients (when EstMdl contains them)

  • Variance parameters (scalar for constant-variance models, or a vector of parameters for a conditional variance model)

  • Degrees of freedom (t innovation distribution only)


expand all

Print the results from estimating an ARIMA 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,...
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,EstParamCov] = estimate(Mdl,Y,'print',false);

Print the estimation results.

    ARIMA(1,0,1) Model:
    Conditional Probability Distribution: Gaussian

                                  Standard          t     
     Parameter       Value          Error       Statistic 
    -----------   -----------   ------------   -----------
     Constant      0.0445373     0.0460376       0.967412
        AR{1}       0.822892     0.0711631        11.5635
        MA{1}        0.12032      0.101817        1.18173
     Variance       0.133727     0.0178793         7.4794

Print the results of estimating an ARIMAX model.

Load the Credit Defaults data set, assign the response IGD to Y and the predictors AGE, CPF, and SPR to the matrix X, and obtain the sample size T. To avoid distraction from the purpose of this example, assume that all predictor series are stationary.

load Data_CreditDefaults
X = Data(:,[1 3:4]);
T = size(X,1);
y = Data(:,5);

Separate the initial values from the main response and predictor series.

y0 = y(1);
yEst = y(2:T);
XEst = X(2:end,:);

Set the ARIMAX(1,0,0) model to MdlY to fit to the data.

MdlY = arima(1,0,0);

Fit the model to the data and specify the initial values.

[EstMdl,EstParamCov] = estimate(MdlY,yEst,'X',XEst,...

Print the estimation results.

    ARIMAX(1,0,0) Model:
    Conditional Probability Distribution: Gaussian

                                  Standard          t     
     Parameter       Value          Error       Statistic 
    -----------   -----------   ------------   -----------
     Constant      -0.204768      0.266078      -0.769578
        AR{1}      -0.017309      0.565618      -0.030602
        Beta1      0.0239329     0.0218417        1.09574
        Beta2     -0.0124602    0.00749917       -1.66154
        Beta3      0.0680871     0.0745041        0.91387
     Variance     0.00539463    0.00224393         2.4041
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