Returns may show little linear predictability while their variance remains strongly predictable, affecting intervals and risk forecasts.

Base-R simulation; rugarch 1.5-6 is recommended for full estimation.

sigma_t^2 = omega + alpha error_(t-1)^2 + beta sigma_(t-1)^2

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

Variable

Book-validated seeded GARCH simulation.

Model choice

With positive omega, nonnegative alpha/beta, and alpha+beta<1, the standard model has finite unconditional variance.

Calculation

Persistence = 0.98; unconditional volatility = 1.414% per period; half-life is about 34.3 periods.

Interpretation

A volatility shock decays slowly even though raw return signs may remain difficult to predict.

Reasonableness check

Conditional variance is latent; squared return is only a noisy proxy. This is educational model analysis, not financial advice.

A volatility shock decays slowly even though raw return signs may remain difficult to predict. Limitation: Conditional variance is latent; squared return is only a noisy proxy. This is educational model analysis, not financial advice.

Illustrative conditional volatility decays slowly after a shock.

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.

Model volatility clustering with conditional variance recursions and distribution-aware diagnostics.

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

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