Single Series ARIMA - Advanced Tab

Select the Advanced tab of the Single Series ARIMA dialog box to access the options described here.

Element Name Description
ARIMA model parameters Use the options under ARIMA model parameters to select at least one seasonal or non-seasonal moving average or autoregressive parameter. If seasonal parameters are specified, a seasonal lag must also be specified.
Estimate constant Select the Estimate constant check box to include a constant in the ARIMA model. In addition to the autoregressive and moving average parameters, ARIMA models may also include a constant. The interpretation of a (statistically significant) constant depends on the model that is fit. Specifically, (1) if there are no autoregressive parameters in the model, then the expected value of the constant is μ, the mean of the series; (2) if there are autoregressive parameters in the series then the constant represents the intercept. If the series is differenced, then the constant represents the mean or intercept of the differenced series; For example, if the series is differenced once, and there are no autoregressive parameters in the model, then the constant represents the mean of the differenced series, and therefore the linear trend slope of the un-differenced series.
Seasonal lag Enter a value in the Seasonal lag box to determine the seasonal lag that is applied to the seasonal autoregressive and/or moving average parameters (option P-Seasonal and Q-Seasonal, respectively). Note that for very long seasonal lags (e.g., 365 days per year), it is recommended to use the Approximate rather than Exact maximum likelihood method, which is less efficient in those cases (see Estimation method below). Refer to the Overview for a discussion of the different methods for computing the likelihood for ARIMA models.
p - Autoregressive Enter a value in the p - Autoregressive box to specify the number of autoregressive parameters in the model.
P - Seasonal Enter a value in the P - Seasonal box to specify the number of seasonal autoregressive parameters in the model. If any seasonal parameters are selected, a Seasonal lag must also be specified.
q - Moving aver Enter a value in the q - Moving aver. box to specify the number of moving average parameters in the model.
Q - Seasonal Enter a value in the Q - Seasonal box to specify the number of seasonal moving average parameters in the model. If any seasonal parameters are selected, a Seasonal lag must also be specified.
Transform variable (series) prior to analysis The transformations selected via the Transform variable (series) prior to analysis group box are performed prior to the analysis, and the ARIMA parameters are estimated for the transformed series. Before forecasts are computed, those transformations will be "undone" and, therefore, those forecasts can be interpreted in terms of the metric of the untransformed series. Click the Other transformations & plots button (see below) to display the Transformations of Variables dialog box, which contains options for transformations that will not automatically be undone when forecasts are computed.
Natural log Select the Natural log check box to compute the natural log for each value.
Power transform When the Power transform check box is selected, each value in the series is raised to the power of C, where C is the value specified in the box adjacent to the Power transform check box.
Difference When the Difference check box is selected, the series is differenced. In keeping with the standard notation introduced by Box & Jenkins (1976), non-seasonal (1) and seasonal (2) differencing can be requested. Specify the respective Lag and the number of difference passes that are to be performed in the adjacent boxes.
Other transformations & plots Click the Other transformations & plots button to display the Transformations of Variables dialog box, which contains options to perform a wide variety of transformations on the data. The transformed series will be appended to the active work area.
Estimation method Use the options in the Estimation method group box to select the procedure for estimating the ARIMA model parameters. In general, the estimation procedure will maximize the likelihood of the data, given the respective model (i.e., number and type of ARIMA parameters). Three different approaches are implemented in the Time Series module for computing the likelihood for an ARIMA model: (1) Approximate (McLeod & Sales) - the approximate maximum likelihood method according to McLeod and Sales (1983), (2) Backcast cases - the approximate maximum likelihood method with backcasting, and (3) Exact (Melard) - the exact maximum likelihood method according to Melard (1984). All methods usually yield similar parameter estimates. Also, all methods are about equally efficient in most real-world time series applications. See the Overview for more information on the procedure for estimating the ARIMA model parameters.
Approximate (McLeod & Sales) Approximate (McLeod & Sales) (approximate maximum likelihood, no backcasts) is the fastest estimation method, and should be used in particular for very long time series (e.g., with more than 30,000 observations; note that the Time Series module is unique in that it will take full advantage of your computer's memory, and it will not impose fixed limitations on the lengths of time series that can be analyzed).
Backcast cases The Backcast cases estimation method is somewhat slower than the Approximate maximum likelihood method without backcasts; however, usually when the N of the series is relatively small and/or some parameter values are close to 1.0 (or -1.0) the estimates derived in this manner tend to be closer to the equivalent Exact maximum likelihood parameters. The optimum setting of this parameter depends on the type of model and the actual magnitude of the parameter values; in practice, McLeod and Sales (1983) recommend to specify the number of backcasts so that:

No.of backcasts = q+s*qs + 20*(p+s*ps)

where p, ps, q, and qs are the non-seasonal and seasonal autoregressive and moving average parameters, respectively, and s is the seasonal lag. Note that the Backcast cases box is only available if the Approximate method is selected.

Exact (Melard) Exact (Melard), Melard's exact maximum likelihood method, can become inefficient when used to estimate parameters for seasonal models with long seasonal lags (e.g., with yearly lags of 365 days). On the other hand, the Time Series module will always use the approximate maximum likelihood method first in order to establish initial parameter estimates that are very close to the actual final values. Therefore, usually only a few iterations with the exact maximum likelihood method are necessary to finalize the parameter estimates.
Estimation options The options in the Estimation options group box pertain to some technical aspect of the parameter estimation procedure. Usually, the default settings do not need to be changed unless the model that you are trying to fit is "unusual" in some way and the settings do not produce valid parameter estimates. In general, parameter estimation of ARIMA models is an iterative procedure. In each iteration, STATISTICA will compute the conditional sums of squares for the current parameter values (refer to the Overview for a description of the approximate and exact maximum likelihood methods for estimating the conditional sums of squares). The goal of the estimation procedure is to find a set of parameters that minimize the sums of squares.

The quasi-Newton method (see Fletcher & Powell, 1963; Fletcher, 1969) is used to minimize the sums of squares. This method does not require explicit derivatives of the function to be minimized, but will approximate them via differencing. Therefore, this is a very efficient general method. Refer to the Nonlinear Estimation module for additional details concerning the estimation of non-linear models. Iterations will continue until 1) the Maximum number of iterations (see below) have been exceeded (note that you can then request additional iterations and the procedure will continue where it left off; thus there is no point in requesting very many iterations in this dialog box), or 2) the parameter accuracy is less than the Convergence criterion (see below).

Maximum number of iterations The value entered in the Maximum number of iterations box determines the maximum number of quasi-Newton iterations that will be performed. When the maximum number of iterations is exceeded during estimation, you are prompted and asked whether to perform additional iterations.
Convergence criterion (required accuracy) The value entered in the Convergence criterion (required accuracy) box determines the accuracy or precision with which the parameters will be estimated, or more specifically, the accuracy of the parameters with respect to the minimum of the conditional SS as computed by the respective approximate or exact maximum likelihood method (refer to the Overview). The estimation procedure will terminate when the changes in the ARIMA parameters over consecutive iterations are less than this value.
Max. no. of iterations for backcasting. The value entered in the Max. no. of iterations for backcasting box determines the maximum number of  iterations that will be performed for backcasting.
User-defined start values Select the User-defined start values check box and click the adjacent    button to display the Specify start values dialog box, in which you specify start values for the parameter estimation.