ARIMA Modeling

Autoregressive integrated moving-average (ARIMA) models are useful for a wide variety of time series analyses, including forecasting, quality control, seasonal adjustment, and spectral estimation, as well as providing summaries of the data.

To fit an ARIMA model

Choose Statistics __image\ebd_ebd86.gif Time Series __image\ebd_ebd87.gif ARIMA Models. The dialog shown below appears.

Model page

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In the ARIMA Modeling dialog, the Model page has the following options:

Data

Data Set

Select or enter the name of a data set having time series as columns.

Variable

Select the column containing the time series to be analyzed or modeled.

Tip You can enter the name of a time series object directly in Time Series. For example, enter lynx to compute the correlogram for the lynx time series.

ARIMA Model Order

Autoregressive (p) Enter an integer giving the order of the autoregressive operator.

Difference (d) Enter an integer giving the number of differences.

Moving Average (q) Enter an integer giving the order of the moving average.

ARIMA Model Periodicity

Seasonality Select the period of the seasonal operator.

Period Select the period of the seasonal operator of the ARIMA model. This field is needed if Seasonality is Other.

Initial Parameters

Enter Initial Parameter Values Select this to enable the input of initial AR coefficients and MA coefficients.

AR coefficients Enter the vector of initial values for the AR coefficients to be used by the optimizer. This must have length equal to p, the order of the autoregressive operator. The default is zero for initial values.

MA coefficients Enter the vector of initial values for the MA coefficients to be used by the optimizer. This must have length equal to q, the order of the autoregressive operator. The default is zero for initial values.

Other Predictors

Add a Covariate Select this to include other covariates in the model.

Variable Enter the name or expression for a univariate or multivariate time series or a vector or matrix. These are used as additive regression variables.

Results

Save As

Enter the name for the object in which to save the results of the analysis.

Print Results

Select this to print out the results of the analysis in the designated output window.

Options page

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In the ARIMA Modeling dialog, the Options page has the following options:

Maximum Numbers

Iterations Enter the maximum number of iterations permitted by the optimizer in computing the parameters of the model. The default is 15.

Likelihood Evals Enter the maximum number of times that the likelihood should be evaluated. The default is 30.

Diagnostics page

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In the ARIMA Modeling dialog, the Diagnostics page has the following options:

Save Diagnostics

Save As Enter the name for the object in which to save the results of the analysis. See the online Help for arima.diag to find out more about the contents of this object. If an object with this name already exists, its contents are overwritten. This must be a valid S-PLUS object name-any combination of alphanumeric characters that starts with an alpha character is allowed. The only non-alphanumeric character allowed is the period ".". Names are case-sensitive, so X and x are different names.

Autocorrelation of Residuals Select to save the autocorrelation of the residuals.

Portmanteau Statistic Select to save a list representing the Portmanteau goodness of fit statistic.

Residuals Select to save residuals.

Standardized Residuals Select to save the standardized residuals.

Plots

Plot Diagnostics

Select to generate a standard plot of diagnostics. See the online Help for arima.diag.plot for details on the different plot components.

Forecast page

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In the ARIMA Modeling dialog, the Forecast page has the following options:

Parameters

Time Periods To Forecast Enter the number of time periods to forecast beyond the end of the series. The default is 5.

Innovations Variance (optional) Enter the estimated innovations variance if different than the concentrated prediction error variance computed from the model.

Plots

Plot Forecast

Select if a plot is desired.

Save Forecast As

Enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. This must be a valid S-PLUS object name-any combination of alphanumeric characters that starts with an alpha character is allowed. The only non-alphanumeric character allowed is the period ".". Names are case-sensitive, so X and x are different names. The saved object is a list with two components: the estimated mean of the forecasts, and the approximate forecast error. This is only saved when a string is entered in the Save As field.

Related S-Plus language functions

acf, ar, arima.mle, arima.diag, arima.diag.plot, arima.forecast, menuArima