# dfCorTest: Testing for Correlations between Subsequent Development... In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

## Description

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

## Usage

 `1` ```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 ≤q n+1-i; i=1,…,m; m≥q 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

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 `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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 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. ```