An employment analyst studies the trends in employment in three industries across five years (60 months). The analyst performs ARIMA to fit a model for the trade industry.

  1. Open the sample data, EmploymentTrends.MTW.
  2. Choose Stat > Time Series > ARIMA.
  3. In Series, enter Trade.
  4. In Autoregressive, under Nonseasonal, enter 1.
  5. Click Graphs, then select ACF of residuals.
  6. Click OK.

Interpret the results

The autoregressive term has a p-value that is less than the significance level of 0.05. The analyst concludes that the coefficient for the autoregressive term is statistically different from 0, and keeps the term in the model. The p-values for the Ljung-Box chi-square statistics are all greater than 0.05, and none of the correlations for the autocorrelation function of the residuals are significant. The analyst concludes that the model meets the assumption that the residuals are independent.

Estimates at Each Iteration

IterationSSEParameters
0543.9080.10090.090
1467.180-0.050105.068
2412.206-0.200120.046
3378.980-0.350135.024
4367.545-0.494149.372
5367.492-0.503150.341
6367.492-0.504150.410
7367.492-0.504150.415
Relative change in each estimate less than 0.001

Final Estimates of Parameters

TypeCoefSE CoefT-ValueP-Value
AR   1-0.5040.114-4.420.000
Constant150.4150.325463.340.000
Mean100.0000.216   
Number of observations:  60

Residual Sums of Squares

DFSSMS
58366.7336.32299
Back forecasts excluded

Modified Box-Pierce (Ljung-Box) Chi-Square Statistic

Lag12243648
Chi-Square4.0512.1325.6232.09
DF10223446
P-Value0.9450.9550.8490.940