The project here is about cleaning covariance matrix. The objective is to estimate the covariance matrix of a matrix of return with N row and T column. T represent the days, and N represent different asset. Our problem is multiple :

• When q=T/N small the usual estimator (MLE for instance) are very noisy. To solve that issue we can use a ledoit et peché Quadratic Invariant Shrinkage to reduce the noise of the eigenvalues.
• Missing value, what's new here is the fact that the matrix of return has missing value. That being said we still need to estimate a covariance matrix. Classical estimator will provide a non positive define matrix, which would mean negative risk in some investment direction. We thus need to inovate with a new kind of cleaning the matrix. For that purpose we will implement a Neural Network (made of a GRU and dense layers) that we will train for different T and Q. To train we will implement a covariance matrix generator (from a wishart distribution) which will create a return matrix which will, in which we will remove some value according to a monotone missingness pattern (miss until nerver miss). From thos return matrix we estimate a covariance matrix which we clean through our NN. We compute a loss and minimize it