Pure prem exponential trend

[piemedia]

Dear friends, please show me how to calculate the exponential trend factor for Pure prem. In "Basic ratemaking", page 352 (A-15):

yr ending Q - X Pure prem

2014-4 60.03
2015-1 60.49
2015-2 60.86
2015-3 61.37
2015-4 61.28


then; pure premium exponential trend at 4 pt is 1.9%. How do you get the 1.9%?


Many thank you!!

[Vorian Atreides]

Place the last 4 points in your TI-30X 2-variable statistic analysis, but use ln(y) instead of y.

The slope of this regression (I get a = 0.004727136) is the quarterly trend.

So, (1 + a)^4 - 1 = 0.0190 or 1.9%.

(Alternately, you could use the regression formula to calculate the model results at 2015-4 and 2016-4--I get 61.43 and 62.61, respectively--and calculate the trend from these two points.)

[piemedia]

Place the last 4 points in your TI-30X 2-variable statistic analysis, but use ln(y) instead of y.

The slope of this regression (I get a = 0.004727136) is the quarterly trend.

So, (1 + a)^4 - 1 = 0.0190 or 1.9%.

(Alternately, you could use the regression formula to calculate the model results at 2015-4 and 2016-4--I get 61.43 and 62.61, respectively--and calculate the trend from these two points.)

Sorry to ask!! How did you get the a=0.004727136? Thank you very much in advance.

[piemedia]

Sorry to ask!! How did you get the a=0.004727136? Thank you very much in advance.

Did you use a= (E(xy)-E(x)E(y) )/( E(x^2)-E(x)^2 ) ?

[M^3]

http://www.actuarialoutpost.com/actuarial_discussion_forum/showpost.php?p=5003501&postcount=2

[M^3]

What's funny about my link is two things:

- Vorian answered almost the same question before
- It's almost exactly the one-year anniversary of that post.

[Vorian Atreides]

:lol: I forgot about that post.

[Vorian Atreides]

Did you use a= (E(xy)-E(x)E(y) )/( E(x^2)-E(x)^2 ) ?
I pushed 2nd STAT, selected two-variable.

Pushed Data, entered 1 for x1, ln(60.49) for y1; proceed in a similar manner for the next three data points.

Press STATVAR. Press the left arrow until the value for a appears.