## Specifying Lag Operator Polynomials Interactively

Consider building a predictive, 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.

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 lags 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 degrees of integration as`0`

,`1`

, or`2`

, or click the appropriate arrow on .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.