Forecasts depend on how information persists. Stable lag relationships make the past informative about the future.

Base stats; tseries and urca are optional for formal tests.

yt = c + phi y(t-1) + error_t; stationarity requires |phi| < 1

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

Variable

Two seeded 180-observation simulations.

Model choice

AR(1) shocks decay geometrically when the coefficient magnitude is below one.

Calculation

The book's validated run produced sample lag-one ACF 0.691 and fitted AR coefficient 0.689 for a generating value of 0.72.

Interpretation

Finite-sample estimates do not equal the generating value exactly; persistence is visible as runs above and below the mean.

Reasonableness check

ACF/PACF patterns suggest candidates but do not replace likelihood, residual diagnostics, and forecast evaluation.

Finite-sample estimates do not equal the generating value exactly; persistence is visible as runs above and below the mean. Limitation: ACF/PACF patterns suggest candidates but do not replace likelihood, residual diagnostics, and forecast evaluation.

AR(1) retains much more lag-one correlation than white noise.

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.

Use stationarity, ACF, PACF, and simple AR/MA models to describe persistence.

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

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