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The ARIMA Procedure

Printed Output

The ARIMA procedure produces printed output for each of the IDENTIFY, ESTIMATE, and FORECAST statements. The output produced by each ARIMA statement is described in the following sections.

IDENTIFY Statement Printed Output

The printed output of the IDENTIFY statement consists of the following:

  1. a table of summary statistics, including the name of the response variable, any specified periods of differencing, the mean and standard deviation of the response series after differencing, and the number of observations after differencing
  2. a plot of the sample autocorrelation function for lags up to and including the NLAG= option value. Standard errors of the autocorrelations also appear to the right of the autocorrelation plot if the value of LINESIZE= option is sufficiently large. The standard errors are derived using Bartlett's approximation (Box and Jenkins 1976, p. 177). The approximation for a standard error for the estimated autocorrelation function at lag k is based on a null hypothesis that a pure moving-average Gaussian process of order k-1 generated the time series. The relative position of an approximate 95% confidence interval under this null hypothesis is indicated by the dots in the plot, while the asterisks represent the relative magnitude of the autocorrelation value.
  3. a plot of the sample inverse autocorrelation function. See the section "The Inverse Autocorrelation Function" for more information on the inverse autocorrelation function.
  4. a plot of the sample partial autocorrelation function
  5. a table of test statistics for the hypothesis that the series is white noise. These test statistics are the same as the tests for white noise residuals produced by the ESTIMATE statement and are described in the section "Estimation Details" earlier in this chapter.
  6. if the CROSSCORR= option is used, a plot of the sample cross-correlation function for each series specified in the CROSSCORR= option. If a model was previously estimated for a variable in the CROSSCORR= list, the cross correlations for that series are computed for the prewhitened input and response series. For each input variable with a prewhitening filter, the cross-correlation report for the input series includes
    1. a table of test statistics for the hypothesis of no cross correlation between the input and response series
    2. the prewhitening filter used for the prewhitening transformation of the predictor and response variables
  7. if the ESACF option is used, ESACF tables are printed
  8. if the MINIC option is used, a MINIC table is printed
  9. if the SCAN option is used, SCAN table is printed
  10. if the STATIONARITY option is used, STATIONARITY tests results are printed

ESTIMATE Statement Printed Output

The printed output of the ESTIMATE statement consists of the following:

  1. when the PRINTALL option is specified, the preliminary parameter estimates and an iteration history showing the sequence of parameter estimates tried during the fitting process
  2. a table of parameter estimates showing the following for each parameter: the parameter name, the parameter estimate, the approximate standard error, t value, approximate probability (Pr > |t|), the lag for the parameter, the input variable name for the parameter, and the lag or "Shift" for the input variable
  3. the estimates of the constant term, the innovation variance (Variance Estimate), the innovation standard deviation (Std Error Estimate), Akaike's information criterion (AIC), Schwarz's Bayesian criterion (SBC), and the number of residuals
  4. the correlation matrix of the parameter estimates
  5. a table of test statistics for hypothesis that the residuals of the model are white noise titled "Autocorrelation Check of Residuals"
  6. if the PLOT option is specified, autocorrelation, inverse autocorrelation, and partial autocorrelation function plots of the residuals
  7. if an INPUT variable has been modeled in such a way that prewhitening is performed in the IDENTIFY step, a table of test statistics titled "Crosscorrelation Check of Residuals." The test statistic is based on the chi-square approximation suggested by Box and Jenkins (1976, pp. 395--396). The cross-correlation function is computed using the residuals from the model as one series and the prewhitened input variable as the other series.
  8. if the GRID option is specified, the sum-of-squares or likelihood surface over a grid of parameter values near the final estimates
  9. a summary of the estimated model showing the autoregressive factors, moving average factors, and transfer function factors in back shift notation with the estimated parameter values.

FORECAST Statement Printed Output

The printed output of the FORECAST statement consists of the following:

  1. a summary of the estimated model
  2. a table of forecasts, with columns for the observation numbers (Obs), the forecast values (Forecast), the forecast standard errors (Std Error), lower and upper limits of the approximate 95% confidence interval (95% confidence limits). The ALPHA= option can be used to change the confidence interval for forecasts. If the PRINTALL option is specified, the forecast table also includes columns for the actual values of the response series (Actual) and the residual values (Residual), and the table includes the input observations used to estimate the model.

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Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.