Quadratic Discriminant Analysis Classifier uses a quadratic function of predictors.
Another assumption that Quadratic Discriminant Analysis uses is the variance of the classes not being equal.
This helps it make it more powerful than the Linear Discriminant Analysis.
Of course both these algorithms assume an underlying Gaussian distribution.
Read this blog post in which I explain how you are going to use Quadratic Discriminant Analysis in making predictions regarding market direction.
First we divide the data into training and testing.
Then we divide the output into classes. The simplest is 2 classes with Up or Down direction.
But I would prefer to make more than 3 classes.
The variance of the classes is not equal.
Market behaves differently when it moves up and when it moves down.