## Testing for Calendar Year Effect

### 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

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 \leq n+1-i; i=1,\ldots,m; m\geq 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

# 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.