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 moving average term has a p-value that is less than the significance level of 0.05. The analyst concludes that the coefficient for the moving average 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.

ARIMA Model: Trade

Estimates at Each Iteration Iteration SSE Parameters 0 543.908 0.100 90.090 1 467.180 -0.050 105.068 2 412.206 -0.200 120.046 3 378.980 -0.350 135.024 4 367.545 -0.494 149.372 5 367.492 -0.503 150.341 6 367.492 -0.504 150.410 7 367.492 -0.504 150.415 Relative change in each estimate less than 0.001
Final Estimates of Parameters Type Coef SE Coef T-Value P-Value AR 1 -0.504 0.114 -4.42 0.000 Constant 150.415 0.325 463.34 0.000 Mean 100.000 0.216

Number of observations: 60

Residual Sums of Squares DF SS MS 58 366.733 6.32299 Back forecasts excluded
Modified Box-Pierce (Ljung-Box) Chi-Square Statistic Lag 12 24 36 48 Chi-Square 4.05 12.13 25.62 32.09 DF 10 22 34 46 P-Value 0.945 0.955 0.849 0.940
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