## Share Results of Econometric Modeler App Session

This example shows how to share the results of an Econometric Modeler app session by:

Exporting time series and model variables to the MATLAB

^{®}WorkspaceGenerating MATLAB plain text and live functions to use outside the app

Generating a report of your activities on time series and estimated models

During the session, the example transforms and plots data, runs
statistical tests, and estimates a multiplicative seasonal ARIMA model. The data set `Data_Airline.mat`

contains monthly counts of airline passengers.

### Import Data into Econometric Modeler

At the command line, load the `Data_Airline.mat`

data set.

`load Data_Airline`

At the command line, open the Econometric Modeler app.

econometricModeler

Alternatively, open the app from the apps gallery (see Econometric Modeler).

Import `DataTimeTable`

into the app:

On the

**Econometric Modeler**tab, in the**Import**section, click the**Import**button .In the Import Data dialog box, in the

**Import?**column, select the check box for the`DataTimeTable`

variable.Click

**Import**.

The variable `PSSG`

appears in the **Time
Series** pane, its value appears in the
**Preview** pane, and its time series plot appears in the
**Time Series Plot(PSSG)** figure window.

The series exhibits a seasonal trend, serial correlation, and possible exponential growth. For an interactive analysis of serial correlation, see Detect Serial Correlation Using Econometric Modeler App.

### Stabilize Series

Address the exponential trend by applying the log transform to
`PSSG`

.

In the

**Time Series**pane, select`PSSG`

.On the

**Econometric Modeler**tab, in the**Transforms**section, click**Log**.

The transformed variable `PSSGLog`

appears in the **Time Series** pane, and its time series plot
appears in the **Time Series Plot(PSSGLog)** figure
window.

The exponential growth appears to be removed from the series.

Address the seasonal trend by applying the 12th order seasonal difference.
With `PSSGLog`

selected in the **Time
Series** pane, on the **Econometric Modeler** tab,
in the **Transforms** section, set
**Seasonal** to `12`

. Then, click
**Seasonal**.

The transformed variable `PSSGLogSeasonalDiff`

appears in the **Time Series** pane, and its time series plot
appears in the **Time Series Plot(PSSGLogSeasonalDiff)** figure
window.

The transformed series appears to have a unit root.

Test the null hypothesis that `PSSGLogSeasonalDiff`

has a unit root by using the Augmented Dickey-Fuller test. Specify that the
alternative is an AR(0) model, then test again specifying an AR(1) model. Adjust
the significance level to 0.025 to maintain a total significance level of 0.05.

With

`PSSGLogSeasonalDiff`

selected in the**Time Series**pane, on the**Econometric Modeler**tab, in the**Tests**section, click**New Test**>**Augmented Dickey-Fuller Test**.On the

**ADF**tab, in the**Parameters**section, set**Significance Level**to`0.025`

.In the

**Tests**section, click**Run Test**.In the

**Parameters**section, set**Number of Lags**to`1`

.In the

**Tests**section, click**Run Test**.

The test results appear in the **Results** table of the
**ADF(PSSGLogSeasonalDiff)** document.

Both tests fail to reject the null hypothesis that the series is a unit root process.

Address the unit root by applying the first difference to
`PSSGLogSeasonalDiff`

. With
`PSSGLogSeasonalDiff`

selected in the
**Time Series** pane, click the **Econometric
Modeler** tab. Then, in the **Transforms**
section, click **Difference**.

The transformed variable `PSSGLogSeasonalDiffDiff`

appears in the **Time Series** pane, and its time series plot
appears in the **Time Series Plot(PSSGLogSeasonalDiffDiff)**
figure window.

In the **Time Series** pane, rename the
`PSSGLogSeasonalDiffDiff`

variable by clicking it
twice to select its name and `PSSGStable`

.

The app updates the names of all documents associated with the transformed series.

### Identify Model for Series

Determine the lag structure for a conditional mean model of the data by plotting the sample autocorrelation function (ACF) and partial autocorrelation function (PACF).

With

`PSSGStable`

selected in the**Time Series**pane, click the**Plots**tab, then click**ACF**.Show the first 50 lags of the ACF. On the

**ACF**tab, set**Number of Lags**to`50`

.Click the

**Plots**tab, then click**PACF**.Show the first 50 lags of the PACF. On the

**PACF**tab, set**Number of Lags**to`50`

.Drag the

**ACF(PSSGStable)**figure window above the**PACF(PSSGStable)**figure window.

According to [1], the
autocorrelations in the ACF and PACF suggest that the following
SARIMA(0,1,1)×(0,1,1)_{12} model is appropriate for
`PSSGLog`

.

$$(1-L)\left(1-{L}^{12}\right){y}_{t}=\left(1+{\theta}_{1}L\right)\left(1+{\Theta}_{12}{L}^{12}\right){\epsilon}_{t}.$$

Close all figure windows.

### Specify and Estimate SARIMA Model

Specify the SARIMA(0,1,1)×(0,1,1)_{12} model.

In the

**Time Series**pane, select the`PSSGLog`

time series.On the

**Econometric Modeler**tab, in the**Models**section, click the arrow to display the models gallery.In the models gallery, in the

**ARMA/ARIMA Models**section, click**SARIMA**.In the SARIMA Model Parameters dialog box, on the

**Lag Order**tab:**Nonseasonal**sectionSet

**Degrees of Integration**to`1`

.Set

**Moving Average Order**to`1`

.Clear the

**Include Constant Term**check box.

**Seasonal**sectionSet

**Period**to`12`

to indicate monthly data.Set

**Moving Average Order**to`1`

.Select the

**Include Seasonal Difference**check box.

Click

**Estimate**.

The model variable `SARIMA_PSSGLog`

appears in the
**Models** pane, its value appears in the
**Preview** pane, and its estimation summary appears in the
**Model Summary(SARIMA_PSSGLog)** document.

### Export Variables to Workspace

Export `PSSGLog`

,
`PSSGStable`

, and
`SARIMA_PSSGLog`

to the MATLAB Workspace.

On the

**Econometric Modeler**tab, in the**Export**section, click .In the Export Variables dialog box, select the

**Select**check boxes for the`PSSGLog`

and`PSSGStable`

time series, and the`SARIMA_PSSGLog`

model (if necessary). The app automatically selects the check boxes for all variables that are highlighted in the**Time Series**and**Models**panes.Click

**Export**.

At the command line, list all variables in the workspace.

whos

Name Size Bytes Class Attributes Data 144x1 1152 double DataTable 144x2 3525 table DataTimeTable 144x1 3311 timetable Description 22x54 2376 char PSSGLog 144x1 1152 double PSSGStable 144x1 1152 double SARIMA_PSSGLog 1x1 7963 arima dates 144x1 1152 double series 1x1 162 cell

The contents of `Data_Airline.mat`

, the numeric vectors
`PSSGLog`

and `PSSGStable`

, and the
estimated `arima`

model object
`SARIMA_PSSGLog`

are variables in the workspace.

Forecast the next three years (36 months) of log airline passenger counts
using `SARIMA_PSSGLog`

. Specify the `PSSGLog`

as presample
data.

```
numObs = 36;
fPSSG = forecast(SARIMA_PSSGLog,numObs,'Y0',PSSGLog);
```

Plot the passenger counts and the forecasts.

fh = DataTimeTable.Time(end) + calmonths(1:numObs); figure; plot(DataTimeTable.Time,exp(PSSGLog)); hold on plot(fh,exp(fPSSG)); legend('Airline Passenger Counts','Forecasted Counts',... 'Location','best') title('Monthly Airline Passenger Counts, 1949-1963') ylabel('Passenger counts') hold off

### Generate Plain Text Function from App Session

Generate a MATLAB function for use outside the app. The function returns the
estimated model `SARIMA_PSSGLog`

given
`DataTimeTable`

.

In the

**Models**pane of the app, select the`SARIMA_PSSGLog`

model.On the

**Econometric Modeler**tab, in the**Export**section, click**Export**>**Generate Function**. The MATLAB Editor opens and contains a function named`modelTimeSeries`

. The function accepts`DataTimeTable`

(the variable you imported in this session), transforms data, and returns the estimated SARIMA(0,1,1)×(0,1,1)_{12}model`SARIMA_PSSGLog`

.On the

**Editor**tab, click**Save**>**Save**.Save the function to your current folder by clicking

**Save**in the Select File for Save As dialog box.

At the command line, estimate the
SARIMA(0,1,1)×(0,1,1)_{12} model by passing
`DataTimeTable`

to `modelTimeSeries`

. Name
the model `SARIMA_PSSGLog2`

. Compare the estimated model to
`SARIMA_PSSGLog`

.

SARIMA_PSSGLog2 = modelTimeSeries(DataTimeTable); summarize(SARIMA_PSSGLog) summarize(SARIMA_PSSGLog2)

ARIMA(0,1,1) Model Seasonally Integrated with Seasonal MA(12) (Gaussian Distribution) Effective Sample Size: 144 Number of Estimated Parameters: 3 LogLikelihood: 276.198 AIC: -546.397 BIC: -537.488 Value StandardError TStatistic PValue _________ _____________ __________ __________ Constant 0 0 NaN NaN MA{1} -0.37716 0.066794 -5.6466 1.6364e-08 SMA{12} -0.57238 0.085439 -6.6992 2.0952e-11 Variance 0.0012634 0.00012395 10.193 2.1406e-24 ARIMA(0,1,1) Model Seasonally Integrated with Seasonal MA(12) (Gaussian Distribution) Effective Sample Size: 144 Number of Estimated Parameters: 3 LogLikelihood: 276.198 AIC: -546.397 BIC: -537.488 Value StandardError TStatistic PValue _________ _____________ __________ __________ Constant 0 0 NaN NaN MA{1} -0.37716 0.066794 -5.6466 1.6364e-08 SMA{12} -0.57238 0.085439 -6.6992 2.0952e-11 Variance 0.0012634 0.00012395 10.193 2.1406e-24

As expected, the models are identical.

### Generate Live Function from App Session

Unlike a plain text function, a live function contains formatted text and equations that you can modify by using the Live Editor.

Generate a live function for use outside the app. The function returns the
estimated model `SARIMA_PSSGLog`

given
`DataTimeTable`

.

In the

**Models**pane of the app, select the`SARIMA_PSSGLog`

model.On the

**Econometric Modeler**tab, in the**Export**section, click**Export**>**Generate Live Function**. The Live Editor opens and contains a function named`modelTimeSeries`

. The function accepts`DataTimeTable`

(the variable you imported in this session), transforms data, and returns the estimated SARIMA(0,1,1)×(0,1,1)_{12}model`SARIMA_PSSGLog`

.To ensure the function does not shadow the M-file function, change the name of the function to

`modelTimeSeriesMLX`

.On the

**Live Editor**tab, in the**File**section, click**Save**>**Save**.Save the function to your current folder by clicking

**Save**in the Select File for Save As dialog box.

At the command line, estimate the
SARIMA(0,1,1)×(0,1,1)_{12} model by passing
`DataTimeTable`

to `modelTimeSeriesMLX`

.
Name the model `SARIMA_PSSGLog2`

. Compare the estimated model
to `SARIMA_PSSGLog`

.

SARIMA_PSSGLog2 = modelTimeSeriesMLX(DataTimeTable); summarize(SARIMA_PSSGLog) summarize(SARIMA_PSSGLog2)

ARIMA(0,1,1) Model Seasonally Integrated with Seasonal MA(12) (Gaussian Distribution) Effective Sample Size: 144 Number of Estimated Parameters: 3 LogLikelihood: 276.198 AIC: -546.397 BIC: -537.488 Value StandardError TStatistic PValue _________ _____________ __________ __________ Constant 0 0 NaN MA{1} -0.37716 0.066794 -5.6466 1.6364e-08 SMA{12} -0.57238 0.085439 -6.6992 2.0952e-11 Variance 0.0012634 0.00012395 10.193 2.1406e-24 ARIMA(0,1,1) Model Seasonally Integrated with Seasonal MA(12) (Gaussian Distribution) Effective Sample Size: 144 Number of Estimated Parameters: 3 LogLikelihood: 276.198 AIC: -546.397 BIC: -537.488 Value StandardError TStatistic PValue _________ _____________ __________ __________ Constant 0 0 NaN NaN MA{1} -0.37716 0.066794 -5.6466 1.6364e-08 SMA{12} -0.57238 0.085439 -6.6992 2.0952e-11 Variance 0.0012634 0.00012395 10.193 2.1406e-24

As expected, the models are identical.

### Generate Report

Generate a PDF report of all your actions on the
`PSSGLog`

and `PSSGStable`

time series, and the `SARIMA_PSSGLog`

model.

On the

**Econometric Modeler**tab, in the**Export**section, click**Export**>**Generate Report**.In the Select Variables for Report dialog box, select the

**Select**check boxes for the`PSSGLog`

and`PSSGStable`

time series, and the`SARIMA_PSSGLog`

model (if necessary). The app automatically selects the check boxes for all variables that are highlighted in the**Time Series**and**Models**panes.Click

**OK**.In the Select File to Write dialog box, navigate to the

`C:\MyData`

folder.In the

**File name**box, type`SARIMAReport`

.Click

**Save**.

The app publishes the code required to create
`PSSGLog`

, `PSSGStable`

,
and `SARIMA_PSSGLog`

in the PDF
`C:\MyData\SARIMAReport.pdf`

. The report includes:

A title page and table of contents

Plots that include the selected time series

Descriptions of transformations applied to the selected time series

Results of statistical tests conducted on the selected time series

Estimation summaries of the selected models

## References

[1] Box, George E. P., Gwilym M. Jenkins, and Gregory C. Reinsel. *Time Series Analysis: Forecasting and Control*. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.