# summarize

Display ARIMA model estimation results

## 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

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

## Output Arguments

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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
`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

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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 ```

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 5.7089e-05 AR{1} 0.13816 0.019893 6.945 3.7845e-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 5.7089e-05 AR{1} 0.13816 0.019893 6.945 3.7845e-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 ```