## Specifying Univariate Lag Operator Polynomials Interactively

Consider building a predictive, univariate time series model (conditional mean,
conditional variance, or regression model with ARMA errors) by using the **Econometric
Modeler** app. After you choose candidate models for estimation (see Perform Exploratory
Data Analysis), you can specify the model structure of each. To do so, on the
**Econometric Modeler** tab, in the **Models**
section, click a model or display the gallery of supported models and click the model
you want.

After you select a time series model, the dialog box appears, where

`Type`

Model Parameters*is the model type. For example, if you select*

`Type`

**SARIMAX**, then the

**SARIMAX Model Parameters**dialog box appears.

For all dynamic models, Econometric Modeler supports two options to specify the lag operator polynomials. The adjustment options are on separate tabs: the

**Lag Order**and**Lag Vector**tab. The**Lag Order**tab options offer a straight forward way to include consecutive lags from lag 1 and degrees of integration (see Specify Lag Structure Using Lag Order Tab). The**Lag Vector**tab options allow you to create flexible models (see Specify Lag Structure Using Lag Vector Tab).The

dialog box contains aModel Parameters`Type`

**Nonseasonal**or**Seasonal**section. The**Seasonal**section is absent in strictly nonseasonal model dialog boxes. To specify the nonseasonal lag operator polynomial structure, use the parameters in the**Nonseasonal**section. To adjust the seasonal lag operator polynomial structure, including seasonality, use the parameters in the**Seasonal**section.To specify the degrees of nonseasonal integration, in the

**Nonseasonal**section, in the**Degree of Integration**box, type the degree, or click the appropriate arrow on .To specify the seasonal periodicity for seasonal models, in the

**Seasonal**section, in the**Period**box, type the periodicity, or click the appropriate arrow on . When the periodicity is greater than 0, you can specify the seasonal autoregressive or moving average polynomial order similarly, and you can specify one degree of seasonal integration by clicking the**Include Seasonal Difference**check box.For verification, the model form appears in the

**Model Equation**section. The model form updates to your specifications in real time.

### Specify Lag Structure Using **Lag Order** Tab

On the **Lag Order** tab, in the **Nonseasonal**
section, you can specify the orders of each lag operator polynomial in the
nonseasonal component. In the appropriate lag polynomial order box (for example, the
**Autoregressive Order** box), type the nonnegative integer
order or click the appropriate arrow on . The app includes all consecutive lags from 1
through

in the polynomial, where
`L`

is the specified
order.`L`

For seasonal models, on the **Lag Order** tab, in the
**Seasonal** section:

Specify the period in the season by entering the nonnegative integer period in the

**Period**box or by clicking .Specify the seasonal lag operator polynomial order. In the appropriate lag polynomial order box (for example, the

**Autoregressive Order**box), type the nonnegative integer order ignoring seasonality or click . The lag operator exponents in the resulting polynomial are multiples of the specified period.

For example, if **Period** is
`12`

and **Autoregressive Order** in the
**Seasonal** section is `3`

, then the
seasonal autoregressive polynomial is $$\left(1-{\Phi}_{4}{L}^{4}-{\Phi}_{8}{L}^{8}-{\Phi}_{12}{L}^{12}\right)$$.

To specify seasonal integration, select the **Include Seasonal
Difference** check box. A seasonal difference polynomial appears in the
**Model Equation** section, and its lag operator exponent is
equal to the specified period.

Consider a SARIMA(0,1,1)×(0,1,2)_{4} model, a seasonal
multiplicative ARIMA model with four periods in a season. To specify this model
using the parameters in the **Lag Order** tab:

Select a time series variable in the

**Time Series**pane.On the

**Econometric Modeler**tab, in the**Models**section, click the arrow >**SARIMA**.In the

**SARIMA Model Parameters**dialog box, on the**Lag Order**tab, enter these values for the corresponding parameters.In the

**Nonseasonal**section, in the**Degree of Integration**box, type`1`

.In the

**Nonseasonal**section, in the**Moving Average Order**box, type`1`

.In the

**Seasonal**section, in the**Period**box, type`4`

. This value indicates a quarterly season.In the

**Seasonal**section, in the**Moving Average Order**box, type`2`

. This action includes seasonal MA lags 4 and 8 in the equation.In the

**Seasonal**section, select the**Include Seasonal Difference**check box.

### Specify Lag Structure Using **Lag Vector** Tab

On the **Lag Vector** tab, you specify the lags in the
corresponding seasonal or nonseasonal lag operator polynomial. This figure shows the
**Lag Vector** tab in the **SARIMA Model
Parameters** dialog box.

To specify the lags that comprise each lag operator polynomial, type a list of
nonnegative, unique integers in the corresponding box. Separate values by commas or
spaces, or use the colon operator (for example, `4:4:12`

).

Specify the seasonal-difference degree by typing a nonnegative integer in the
**Seasonality** box or by clicking .

Consider a SARIMA(0,1,1)×(0,1,2)_{4} model, a seasonal
multiplicative ARIMA model with four periods in a season. To specify this model
using the parameters in the **Lag Vector** tab:

Select a time series variable in the

**Time Series**pane.On the

**Econometric Modeler**tab, in the**Models**section, click the arrow >**SARIMA**.In the

**SARIMA Model Parameters**dialog box, click the**Lag Vector**tab, then enter these values for the corresponding parameters.In the

**Nonseasonal**section, in the**Degree of Integration**box, type`1`

.In the

**Nonseasonal**section, in the**Moving Average Lags**box, type`1`

.In the

**Seasonal**section, in the**Seasonality**box, type`4`

. Therefore, a seasonal-difference polynomial of degree 4 appears in the equation in the**Model Equation**section.In the

**Seasonal**section, in the**Moving Average Lags**box, type`4 8`

. This action includes seasonal MA lags 4 and 8 in the equation.