ARIMA is useful only when preprocessing, candidate comparison, residual diagnostics, and out-of-sample scoring use information available at the forecast origin.

Base stats; forecast 9.0.2 and fable 0.5.0 are optional extensions.

phi(B)(1-B)^d yt = c + theta(B) error_t

1. Step 1Define every variable and unit.
2. Step 2Check assumptions and information timing.
3. Step 3Calculate, verify, and interpret in context.

Variable

A seeded integrated moving process with the final 12 observations held out.

Model choice

ARIMA combines differencing with autoregressive and moving-average dependence.

Calculation

The live result reports holdout RMSE and a Ljung–Box diagnostic; the book's Canadian inflation exercise had RMSE 0.624 and residual p-value 0.00135.

Interpretation

A small p-value signals residual dependence in that book specification rather than a result to hide.

Reasonableness check

One holdout origin is uncertain; rolling origins and naive benchmarks provide stronger evidence.

A small p-value signals residual dependence in that book specification rather than a result to hide. Limitation: One holdout origin is uncertain; rolling origins and naive benchmarks provide stronger evidence.

Intervals widen with horizon in a typical model-based forecast.

Run the self-contained starter code in the protected STATLAB R runner. The code prints an auditable result and avoids network or unrestricted file access.

Compare your result with the definition, units, and model assumptions—not only with a target number.

Complete these without looking at the selected solutions. More than one defensible program may exist.

These are compact solution routes. Confirm dimensions, units, and any changed modelling choices.

Follow an auditable specify–estimate–diagnose–forecast–evaluate loop.

Name the assumption, evidence you would seek, and how the recommendation might change.

Reach 70% to complete the chapter. Explanations appear after submission.