Actuarial Outpost > CAS 2017 Exam 7 #10 a
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#1
02-08-2020, 02:44 PM
 Zver Member Join Date: Apr 2005 Posts: 546
2017 Exam 7 #10 a

Could someone walk me through part a of 2017 Exam 7? I thought that since the residual is (a-e)/e^0.5 and actual is higher and higher than expected as time passes by, the residuals are going to start at 0 and then grow upwards. In other words, first cell for first ay is precisely matching the actual. Then the next diagonal is a bit off (too low). Then the next is off even further. Could someone explain to me why the residuals start as negative on the CAS solution and why they are mentioning overestimating for a part of the triangle and underestimating for another part? Thank you kindly.
#2
02-11-2020, 01:43 AM
 Zver Member Join Date: Apr 2005 Posts: 546

Any help would be greatly appreciated!
#3
02-11-2020, 02:42 AM
 AbedNadir Member CAS SOA Join Date: Mar 2014 Studying for FCAS Posts: 2,780

in order for the first cell in the first AY to precisely match the actual, it would have to be singularly defined. For example, in ODP bootstrap, in the latest AY with the one cell or in the earliest AY in the most mature cell, the parameters are unique in those cells and we observe 0 residuals which you have to be careful with when you bootstrap. This happens because for certain parameter combinations, they are the only cells available to estimate the parameters.

So for the example we are discussing, in a triangle with all values available on N x N, cell (1,1) doesn't get a DY parameter, just an AY parameter assuming you used one, so as long as the first AY has more than one value, the residual can't be 0. If you didn't use any AY parameters, and if you used an intercept in your model then you'd pool across all AYs, so the residual still wouldn't be uniquely defined. If you didn't use an intercept and just DY parameters and you gave the first DY interval a parameter, cell (1,1) isn't uniquely defined either. So there is no way to get a 0 residual in cell (1,1) without using a CY parameter directly on it.

So if it isn't zero, which direction would it be in? Why does it start negative?

As a base case, assume you use one AY parameter and one DY parameter. The AY parameter will try to fit to the average incremental loss across all years as if it's an intercept and the DY parameter will account for most losses happening early and lower and lower amounts coming in at later development periods. These parameters will fit to the averages on the whole triangle.

If you compare cell (1,1) with cell (5,1) for example, cell(5,1) should be less over predicted because it's closer to the average CY. The points that are most under predicted should be those that have had the trend acting the longest, and the points most over predicted should be the points that have had the trend acting for the least.
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Last edited by AbedNadir; 02-11-2020 at 02:45 AM..
#4
02-11-2020, 10:20 PM
 AbedNadir Member CAS SOA Join Date: Mar 2014 Studying for FCAS Posts: 2,780

I hope someone can correct my dumb blog post if I was wrong anywhere
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#5
02-11-2020, 11:18 PM
 examsarehard Member CAS Join Date: May 2011 Posts: 617

You would expect the residuals to be distributed around 0 because even if there is a calendar year trend, the model will still try to get the average level right.

If the residuals started at 0 and were strictly increasing, then the model would be underestimating in every cell, and the expected value would be off.

Since we know the residuals should be distributed around 0 and calendar year trend is increasing, that means the earlier diagonals should be negative and the later diagonals should slope upward.