Thank you for your help everyone, and I apologise beforehand if this is a lousy or dumb question.
I am looking to read up more on Quadratic Loss & Linex Loss, and forecast optimality. In my university text, we were told that the quadratic loss function is essentially the squared-error of the loss function, or square of the difference between actual and forecasted value, as shown below:
We are then told that the Linear-exponential loss function is an asymmetric loss function that tends towards the Quadratic loss function as a tends towards zero, as shown below:
My question is how can the Linex loss function tend towards the quadratic loss function as a tends towards zero? I might be a bit clueless and missing the math here but I can't seem to prove that as a tends towards zero, Linex function tends to Quadratic function.
Any help would be greatly appreciated. Thank you!