dfCorTest {ChainLadder} R Documentation

## Testing for Correlations between Subsequent Development Factors

### Description

One of the main assumptions underlying the chain ladder method is the uncorrelation of subsequest development factor. The function tests this assumption.

### Usage

dfCorTest(Triangle, ci = .5)


### 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

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

The usual test for uncorrelatedness requires that we have identically distributed pairs of observations which come from a Normal distribution. Both conditions are usually not fulfilled for adjacent columns of development factors. Spearman's correlation coefficient is therefore used.

The metric calulated by the procudeure described return a statistic T that it 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

dfCorTest returns a list with the following elements

 T_stat summary statistic Var variance of the resulting distribution Range vector of the range corresponding the confidence interval threshold selected ci confidence interval

### Note

Additional references for further reading:

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

Venter, G.G., Testing the Assumptions of Age-to-Age Factors, Proceedings of the Casualty Actuarial Society LXXXV, 1998, pp. 807-847

### 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

See also qpaid for dealing with non-square triangles, cyEffTest for the test for calendar year effect, chainladder for the chain-ladder method, summary.dfCorTest, plot.dfCorTest

### Examples

# Before actually applying the Chain Ladder technique it is necessary to check
# whether the Development Factors are correlated

# Apply the function to the triangle and save the output into the variable test
test <- dfCorTest(RAA)

# Plot the confidence interval and the test metric
plot(test)

# The metric is within the confidence interval, therefore the Development Factors are nor correlated

# 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 Development Factor Correlation and therefore the chain ladder method
# can be applied.


[Package ChainLadder version 0.2.19 Index]