Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

In graduation of crude mortality rates, which feature of the graduated rates is the serial correlation test (together with the runs test) designed to detect?

The serial correlation test detects clumping of same-signed deviations, meaning runs where the graduated rates stay persistently above or below the crude rates. This shows adherence to the data is poor over ranges of ages, even if overall counts balance, so it complements the sign test.

  1. AClumping of deviations of the same sign, indicating the graduation is biased over stretches of agesCorrect
  2. BExcessive roughness in the third differences of the graduated rates
  3. CToo few individual standardised deviations lying outside plus or minus 1
  4. DA total number of actual deaths that differs from the expected total
  5. Unequal numbers of positive and negative deviations

Explanation

Serial correlation and runs tests look for long sequences of deviations with the same sign, which show the graduated curve lying persistently above or below the crude rates. Smoothness is checked using differences, not these tests. The sign test, not these, counts positive against negative deviations.

Did you get it right without looking?

One question tells you little. A timed set on Graduation and graduation tests shows your real accuracy, how long you take and where you lose marks.

Practise Graduation and graduation testsFree diagnostic mock

More Graduation and graduation tests questions