## Compare Conditional Variance Model Fit Statistics Using Econometric Modeler App

This example shows how to specify and fit GARCH, EGARCH, and GJR
models to data using the Econometric Modeler app. Then, the example determines the
model that fits to the data the best by comparing fit statistics. The data set,
which is stored in `Data_FXRates.mat`

, contains foreign exchange
rates measured daily from 1979–1998.

Consider creating a predictive model for the Swiss franc to US dollar exchange
rate (`CHF`

).

### Import Data into Econometric Modeler

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

data
set.

`load Data_FXRates`

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**.

All time series variables in `DataTimeTable`

appear in the
**Time Series** pane, and a time series plot of all the
series appears in the **Time Series Plot(AUD)** figure
window.

### Plot the Series

Plot the Swiss franc exchange rates by double-clicking the
`CHF`

time series in the **Time
Series** pane.

Highlight periods of recession:

In the

**Time Series Plot(CHF)**figure window, right-click the plot.In the context menu, select

**Show Recessions**.

The `CHF`

series appears to have a stochastic
trend.

### Stabilize the Series

Stabilize the Swiss franc exchange rates by applying the first difference to
`CHF`

.

In the

**Time Series**pane, select`CHF`

.On the

**Econometric Modeler**tab, in the**Transforms**section, click**Difference**.Highlight periods of recession:

In the

**Time Series Plot(CHFDiff)**figure window, right-click the plot.In the context menu, select

**Show Recessions**.

A variable named

`CHFDiff`

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

The series appears to be stable, but it exhibits volatility clustering.

### Assess Presence of Conditional Heteroscedasticity

Test the stable Swiss franc exchange rate series for conditional heteroscedasticity by conducting Engle's ARCH test. Run the test assuming an ARCH(1) alternative model, then run the test again assuming an ARCH(2) alternative model. Maintain an overall significance level of 0.05 by decreasing the significance level of each test to 0.05/2 = 0.025.

In the

**Time Series**pane, select`CHFDiff`

.On the

**Econometric Modeler**tab, in the**Tests**section, click**New Test**>**Engle's ARCH Test**.On the

**ARCH**tab, in the**Parameters**section, set**Number of Lags**of`1`

.Set

**Significance Level**to`0.025`

.In the

**Tests**section, click**Run Test**.Repeat steps 3 through 5, but set

**Number of Lags**to`2`

instead.

The test results appear in the **Results** table of the
**ARCH(CHFDiff)** document.

The tests reject the null hypothesis of no ARCH effects against the
alternative models. This result suggests specifying a conditional variance model
for `CHFDiff`

containing at least two ARCH lags.
Conditional variance models with two ARCH lags are locally equivalent to models
with one ARCH and one GARCH lag. Consider GARCH(1,1), EGARCH(1,1), and GJR(1,1)
models for `CHFDiff`

.

### Estimate GARCH Model

Specify a GARCH(1,1) model and fit it to the
`CHFDiff`

series.

In the

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

time series.Click the

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

**GARCH Models**section, click**GARCH**.In the GARCH Model Parameters dialog box, on the

**Lag Order**tab:Set

**GARCH Degree**to`1`

.Set

**ARCH Degree**to`1`

.Click

**Estimate**.

The model variable **GARCH_CHFDiff** appears in the
**Models** pane, its value appears in the
**Preview** pane, and its estimation summary appears in the
**Model Summary(GARCH_CHFDiff)** document.

### Specify and Estimate EGARCH Model

Specify an EGARCH(1,1) model containing a leverage term at the first lag, and
fit the model to the `CHFDiff`

series.

In the

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

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

**GARCH Models**section, click**EGARCH**.In the EGARCH Model Parameters dialog box, on the

**Lag Order**tab:Set

**GARCH Degree**to`1`

.Set

**ARCH Degree**to`1`

. Consequently, the app includes a corresponding leverage lag. You can remove or adjust leverage lags on the**Lag Vector**tab.

Click

**Estimate**.

The model variable **EGARCH_CHFDiff** appears in the
**Models** pane, its value appears in the
**Preview** pane, and its estimation summary appears in the
**Model Summary(EGARCH_CHFDiff)** document.

### Specify and Estimate GJR Model

Specify a GJR(1,1) model containing a leverage term at the first lag, and fit
the model to the `CHFDiff`

series.

In the

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

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

**GARCH Models**section, click**GJR**.In the GJR Model Parameters dialog box, on the

**Lag Order**tab:Set

**GARCH Degree**to`1`

.Set

**ARCH Degree**to`1`

. Consequently, the app includes a corresponding leverage lag. You can remove or adjust leverage lags on the**Lag Vector**tab.Click

**Estimate**.

The model variable **GJR_CHFDiff** appears in the
**Models** pane, its value appears in the
**Preview** pane, and its estimation summary appears in the
**Model Summary(GJR_CHFDiff)** document.

### Choose Model

Choose the model with the best parsimonious in-sample fit. Base your decision
on the model yielding the minimal Akaike information criterion (AIC). The table
shows the AIC fit statistics of the estimated models, as given in the
**Goodness of Fit** section of the estimation summary of
each model.

Model | AIC |
---|---|

GARCH(1,1) | -28730 |

EGARCH(1,1) | -28726 |

GJR(1,1) | -28737 |

The GJR(1,1) model yields the minimal BIC value. Therefore, it has the best parsimonious in-sample fit of all the estimated models.