How do you create a simulated triangle, and what is it for?

Creating simulated triangles is one way of testing whether you have a 'good' model for your data. If you can't distinguish the real from the simulated data, it is plausible that the model could have produced the real data.

To create a simulated triangle, follow these steps:

1. In PTF, with the appropriate model loaded, choose Test->Simulate Triangles from Model. Choose the number of the simulated triangles you want to create then click Simulate.
2. Click on the Triangle Group tab to return to the Triangle Group window and click on the Models tab.
3. Select the model you just simulated and drag-and-drop it to each of the simulated triangles in the left-hand pane.
4. Select each of the new model/simulated triangle combinations in the right-hand pane and press Ctrl+O. This will take you into PTF with the model loaded for each of the simulated triangles.
   
   

   

5. Compare the residual plots for the simulated triangles with the plots for the original data. They should look similar if the original model is a good model. Also check the Diagnostic Tools and Forecast Summary (Errors and Comparisons) to see if they are similar between the real and simulated data.

We have data for every quarter (or month) of development corresponding to each accident year. Can ICRFS-Plus™ model such a "non-triangular" triangle?

Yes. Although you cannot have a triangle with different periods in the development and accident direction, you can successfully analyse an annual by quarterly triangle (or any other combination of periods). Create a quarterly triangle and copy the data for each accident year into the first quarter of each accident year of the triangle. All intermediate accident quarters should be set to zero (they will be treated as "missing values" as long as you don't change the default triangle property "Manual constant" of zero). Then create an exposure set, assigning the intermediate accident quarters small values (eg, 0.000001) "relative" to the first accident quarters. When you forecast in PTF (or PSCF), the forecasts for the intermediate accident quarters will be zero.

A diagram of part of the triangle is shown below - O represents data and X represents missing values.

Part of the exposure window is shown below (of course you should use whatever exposure information you have in place of the 1000's):

The triangle is set up this way for two reasons. Firstly, so that the residuals versus calendar periods are correct. Secondly, as the diagonal elements are maintained with this method, the calendar trend parameters can be estimated.