ARIMA Models and Forecasting

Fits seasonal and non-seasonal ARIMA (p, d, q)(pS, dS, qS) models to continuous variables; various results graphs, forecasts, and tools for assessing the quality fit to the data are reported by the program.

ARIMA Model

Element Name Description
Autoregressive parameters p Number of nonseasonal autoregressive parameters p in the ARIMA (p, d, q)(pS, dS, qS) model.
Moving average parameters q Number of nonseasonal moving average parameters q in the ARIMA (p, d, q)(pS, dS, qS) model.
Seasonal autoregressive pS Number of seasonal autoregressive parameters pS in the ARIMA (p, d, q)(pS, dS, qS) model.
Seasonal moving average qS Number of seasonal moving average parameters qS in the ARIMA (p, d, q)(pS, dS, qS) model.
Seasonal lag Specifies the seasonal lag that is applied to the seasonal autoregressive and/or moving average parameters (pS, qS).
Estimate ARIMA constant Include a Constant parameter in the model.

Transformations

Element Name Description
Difference series When the Difference is selected, the series is differenced. 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.
Difference series, lag 1 When the Difference is selected, the series is differenced. 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.
Passes, differencing 1 When the Difference is selected, the series is differenced. 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.
Difference series, lag 2 When the Difference is selected, the series is differenced. 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.
Passes, differencing 2 When the Difference is selected, the series is differenced. 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.
Power-transformation Select the Power transformation to raise each value in the series to the power of constant C, where C is the value specified as the power transform parameter. The transformations are performed prior to the analyses, e.g., to stabilize the variance over the series, etc.
Power-transform parameter When the Power-transformation is selected, each value in the series is raised to the power of C, where C is the value specified in this box.
Natural-log transformation Select the Natural-log transformation to compute the natural log for each value. The transformations are performed prior to the analyses, e.g., to stabilize the variance over the series, etc.

Estimation

Element Name Description
Estimation method 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.
Number of backcasts Applicable to the Approximate McLeod and Sales estimation method only; specify a number greater than 0 to request the backcast-cases estimation method; this method may be 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.
Max n iterations, backcasting Specifies the maximum number of iterations for backcasting; not applicable if the Number of backcasts is equal to 0, or if Exact maximum likelihood (ML) estimation is requested.
Max number of iterations Specifies the maximum number of iterations for the iterative parameter estimation procedure.
Convergence criterion Specifies the Convergence criterion (required accuracy) for the iterative parameter estimation procedure; the estimation procedure will terminate when the changes in the ARIMA parameters over consecutive iterations are less than this value.

Results

Element Name Description
Detail of computed results reported Detail of computed results; if Comprehensive results are requested, the autocorrelation function for the residuals, and various additional residual plots are reported; if All results are requested, the original and transformed (for the analysis) series is also displayed and plotted.
Label plots with case names Label the horizontal axis in plots with case numbers or case names (if available).
p; for highlighting Specifies the p value used for highlighting significant results (e.g., parameter estimates) in the in spreadsheets.
White noise standard errors Computes the standard errors for the autocorrelation function for the ARIMA residuals under the assumption that the series is a white noise process.
Number of lags Specifies the maximum number of lags for evaluating the autocorrelation function for the ARIMA residuals.

Forecasting

Element Name Description
Computes ARIMA forecasts Computes and display ARIMA forecasts.
Number Of cases to forecast Number of cases to forecast in the plot of the fitted ARIMA model.
p; for confidence limits Specifies p to compute confidence limits for the ARIMA forecasts.

Missing Data

Element Name Description
Replace missing data Specifies how missing data is to be replaced. Missing data can be replaced by the overall mean, interpolated from adjacent points, replaced by the mean or median of N adjacent points (on both sides of the hole), or estimated (predicted) from linear trend regression.

 Note that as long as the missing data are at the end of the series (trailing missing data) or the beginning of the series (leading missing data), the missing data will simply be ignored.
Number of adjacent points Applicable if missing data are replaced by the mean or median of N adjacent points; specify N.

 The missing data are replaced by the mean or median computed from the N adjacent points on both sides of the hole of missing data.