The LR model of backtesting vis a vis Logit

[QuantMan2318]

Dear @David Harper CFA FRM
I am just curious to know, Jorion's Backtesting talks about Log Likelihood Ratio with
LR = -2*ln[(1-p)^(T-N)*p^N]+2*ln[(1-(N/T)]^(T-N)*(N/T)^N]
Meanwhile, the formula for a Logistic Regression is
(1/m)*sum(-y*log[h]-(1-y)*log[1-h])
Are they in some manner, interrelated?

 

[Taunk]

Dear @QuantMan2318 , I was going through the readings but was facing difficulty in grasping that when is log likelihood ratio used.

Can you let me know its applicability without the math.

 

[QuantMan2318]

Dear @taunk

I think that the Log likelihood ratio is the more advanced version of the basic backtesting that was discussed prior to it. We know that the Backtesting model as initially adopted comprised of the N, which is the number of exceptions as well as the T which is the sample size (number of days), the simple model we adopted actually just provided whether we can/or not reject the model based on the number of exceptions.

However, there is a double edged sword, there is a possibility that we may reject a correct model as the back test we did resulted in a larger than usual number of exceptions, this may purely be an anomaly rather than any problem with the model itself. This is what Jorion calls a Type I error, rejecting a correct model.

Kupiec found out a way to provide a zone in the curve where though the number of exceptions may be large, we may still accept the model. Think of it as a model that provides a range of different exceptions where me may still accept the model within the range

Hope this helped

 

[Taunk]

Thanks@quantman