IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests
A graduation of crude mortality rates has been produced and the standardised deviations z_x are calculated for 30 ages. A test is applied to the lag-1 sample autocorrelation of these z_x to look for a problem in the graduation. Which feature of the graduation does this test mainly detect?
The lag-1 serial correlation test detects clumping of same-signed deviations across neighbouring ages. It checks whether successive standardised deviations are correlated, which shows the graduated curve repeatedly lying on one side of the crude rates. Other tests cover overall bias and individual large deviations.
- AClumping of deviations of the same sign across adjacent agesCorrect
- BOverall bias of the graduated rates above the crude rates
- CIndividual ages with unusually large deviations
- DInsufficient smoothness in the graduated rates
- Wrong choice of the number of parameters in the formula
Explanation
The lag-1 serial correlation test examines whether successive standardised deviations are correlated. Positive correlation shows runs of same-signed deviations, meaning the graduated curve is not following the crude data consistently. Overall bias is tested by the signs test or the cumulative deviations test, and individual large deviations by the chi-square and standardised deviations tests.
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