print

(To be removed) Display parameter estimation results for ARIMA or ARIMAX models

Syntax

print(EstMdl,EstParamCov)

Description

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

Examples

Print ARIMA Estimation Results

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,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,EstParamCov] = estimate(Mdl,Y,Display="off"); 

Print the estimation results.

print(EstMdl,EstParamCov) 

Warning: PRINT will be removed in a future release; use SUMMARIZE instead.

 
    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 ARIMAX Estimation Results

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 $$y_t=c+{\varphi }_1{y}_{t-1}+{\epsilon }_t$$ 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, ...
    Y0=y0,Display="off");

Print the estimation results.

print(EstMdl,EstParamCov) 

Warning: PRINT will be removed in a future release; use SUMMARIZE instead.

 
    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
      Beta(1)      0.0239329     0.0218417        1.09574
      Beta(2)     -0.0124602    0.00749917       -1.66154
      Beta(3)      0.0680871     0.0745041        0.91387
     Variance     0.00539463    0.00224393         2.4041

Input Arguments

EstMdl — Estimated ARIMA or ARIMAX model

arima model object

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

EstParamCov — Estimated error variance-covariance matrix

square matrix

Estimated error variance-covariance matrix as returned by estimate, specified as a square matrix with rows and columns corresponding to parameters known to the optimizer of estimate. Known parameters include all parameters estimate estimated. Rows and columns associated with parameters fixed during estimation contain 0s.

The order of the parameters (that is, rows and columns) in EstParamCov is:

• 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)

Version History

Introduced in R2012a

R2018a: Warns

print will be removed in a future release. Use summarize instead.

This list shows the differences between print and summarize:

• For an unestimated (custom) arima model input, summarize returns the standard object display of the model.

• For an estimated arima model input, as returned by estimate, summarize prints an estimation summary in a MATLAB table and lists other estimation statistics. summarize returns the estimation statistics in an output structure array.