### Signal or noise?

#### (Nov 25, 2016)

Each year since 2009 the CMI in the UK has released a spreadsheet tool for actuaries to use for mortality projections.  I have written about this tool a number of times, including how one might go about setting the long-term rate.  The CMI now wants to change how the spreadsheet is calibrated and has proposed the following model in CMI (2016a):

$\log m_{x,y} = \alpha_x + \beta_x(y-\bar y) + \kappa_y + \gamma_{y-x}\qquad (1)$

which the CMI calls the APCI model.  $$m_x$$ is the central rate of mortality at age $$x$$ in year $$y$$ and $$\alpha_x$$, $$\beta_x$$, $$\kappa_y$$ and $$\gamma_{y-x}$$ are vectors of parameters to be estimated.  $$\bar y$$ is the average year, which is used to centre the time index around…

Tags: CMI, APCI, APC, Lee-Carter, Age-Period, smoothing