# cyEffTest: Testing for Calendar Year Effect In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

## Description

One of the three basic assumptions underlying the chain ladder method is the independence of the accident years. The function tests this assumption.

## Usage

 `1` ```cyEffTest(Triangle, ci = 0.95) ```

## Arguments

 `Triangle` cumulative claims triangle. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix C_{ik} which is filled for k ≤q n+1-i; i=1,…,m; m≥q n , see `qpaid` for how to use (mxn)-development triangles with m

## Details

The main reason why this independence can be violated in practice is the fact that there could be certain calendar year effects such as major changes in claims handling or in case reserving or external influences such as substantial changes in court decisions or inflation.

As described by the Mack's 1994 paper a procedure is designed to test for calendar year influences.

The procedure returns a summary statistic Z which is assumed to be Normally Distributed. It is therefore possible to define a confidence interval threshold in order to evaluate the outcome of the test.

## Value

cyEffTest returns a list with the following elements

 `test_table` complete table of results `Z` summary statistic `E` expected value of the resulting distribution `Var` variance of the resulting distribution `Range` vector of the range corresponding the confidence interval threshold selected `ci` confidence interval

## Note

Thomas Mack. Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin. Vol. 23. No 2. 1993. pp.213:225

Thomas Mack. The standard error of chain ladder reserve estimates: Recursive calculation and inclusion of a tail factor. Astin Bulletin. Vol. 29. No 2. 1999. pp.361:366

## Author(s)

Marco De Virgilis devirgilis.marco@gmail.com

## References

Mack, T., Measuring the Variability of Chain Ladder Reserve Estimates, Casualty Actuarial Society Forum, Spring 1994

See also `qpaid` for dealing with non-square triangles, `dfCorTest` for the test for correlations between subsequent development factors, `chainladder` for the chain-ladder method, `summary.cyEffTest`, `plot.cyEffTest`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# Before actually applying the Chain Ladder technique it is necessary to check # wether the triangle has Calendar Year Effect # Apply the function to the triangle and save the output into the variable test test <- cyEffTest(RAA) # Plot the confidence interval and the test metric plot(test) # The metric is within the confidence interval, therefore the triangle doesn't # have Calendar Year Effect # Print the summary table summary(test) # Print only the main outcomes print(test) # The test has returned a negative outcome. This means that the triangle is # not affected by Caledar Year Effect and therefore the chain ladder method # can be applied. ```

### Example output

```Welcome to ChainLadder version 0.2.11

the overall package documentation.

See demo(package='ChainLadder') for a list of demos.

To suppress this message use:

\$Table
j S_j L_j Z_j n m    E_Zj    Var_Zj
1 2   1   1   1 2 0 0.50000 0.2500000
2 3   3   0   0 3 1 0.75000 0.1875000
3 4   3   1   1 4 1 1.25000 0.4375000
4 5   1   3   1 4 1 1.25000 0.4375000
5 6   1   3   1 4 1 1.25000 0.4375000
6 7   2   4   2 6 2 2.06250 0.6210938
7 8   4   4   4 8 3 2.90625 0.8037109
8 9   4   4   4 8 3 2.90625 0.8037109

\$Totals
Totals
Z      14.000000
E[Z]   12.875000
Var[Z]  3.978516

\$Range
Value
Lower  8.965613
Upper 16.784387

Calendar Year Effect

Z = 14

95%-Range = ( 8.965613 ; 16.78439 )

Calendar Year Effect: FALSE
```

ChainLadder documentation built on Jan. 9, 2022, 5:06 p.m.