An analyst collected data on the number of airline passengers for 108 months. The analyst
wants to use an ARIMA model to generate forecasts for the data. The analyst
previously examined a time series plot of the data and observed that the variation
in the seasonal cycle increases over time. The analyst concluded that a natural log
transformation of the data is appropriate. After the transformation, the analyst
examined the time series plot of the transformed data and the autocorrelation
function (ACF) plot of the transformed data. Both plots suggest that the starting
point for the model is to choose 1 for the order of non-seasonal differencing and 1
for the order of seasonal differencing. The analyst requests forecasts for the next
3 months.
Choose Stat > Time Series > Forecast with Best ARIMA Model.
In Series, enter Number of Passengers.
In Differencing order d, select
1.
Select Fit seasonal models with period and enter
12 for the period.
In Seasonal differencing order D, select
1.
In Number of forecasts, enter
3.
Select Options.
In Box-Cox Transformation, select λ = 0 (natural log).
Select OK in each dialog box.
Interpret the results
The model selection table ranks the models from the search in order by AICc. The ARIMA(0, 1,
1)(1, 1, 0) model has the least AICc. The ARIMA results that follow are for the
ARIMA(0, 1, 1)(1, 1, 0) model.
The p-values in the parameters table show that the model terms are significant at the 0.05 level. The analyst concludes that the coefficients belong in the model. The p-values for the Modified Box-Pierce (Ljung-Box) statistics are all insignificant at the 0.05 level. The ACF of the residuals and the PACF of the residuals show a spike at lag 24. Because a large spike at a high lag number is usually a false positive and the test statistics are all insignificant, the analyst concludes that the model meets the assumption that the residuals are independent. The analyst concludes that examination of the forecasts is reasonable.
* WARNING * Inestimable ARIMA(p, d, q)(P, D, Q) models that do not include a constant term: (2, 1, 1)(1, 1, 1)
