IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests
A graduation has a very good chi-squared fit and passes the sign test, yet the serial correlation test is failed with significantly positive r1. What does this most plausibly imply?
It implies the graduated curve departs systematically from the crude rates over stretches of ages, giving runs of same-signed deviations even though overall counts balance. This is typical of over-smoothing or a poorly shaped graduating formula, which chi-squared and sign tests may fail to reveal.
- AThe graduated rates are too rough
- BThe graduated rates are over-smoothed in places, giving runs of same-signed deviations despite overall balanceCorrect
- CThe crude rates contain no information
- DThe sample has too few lives for any test
- The graduation is certain to be adequate
Explanation
Positive serial correlation means adjacent deviations tend to share the same sign, so the graduated curve lies above or below the crude rates over stretches. Chi-squared and sign tests can still pass because deviations offset overall. Roughness is a smoothness matter, not indicated here.
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