A Machine Learning Model for Estimating High-dimensional Correlation Matrices

Matrice korelacije se koriste za opis međusobne povezanosti varijabli. Problem kod njih nastaje kada je broj varijabli kojima određujemo korelaciju slične veličine kao i broj dostupnih uzoraka mjerenja po varijabli. Standardne metode procjene stvarne korelacije prestaju davati povjerljive rezultate, te moramo pronaći način kako da ih ispravimo. U ovom radu ću se baviti navedenom tematikom korištenjem metoda iz familije modela „Analiza glavnih komponenti“ ili na engleskom „Principal component analysis“, često zvana skraćenim nazivom „PCA“. Navedenim metodama ću ispitati svojstvo procjene i primijeniti ću ih u problemu optimizacije portfelja vrijednosnica.Correlation matrix describes the relation between measured variables. When number of available data points we gather are similar in size or larger than the number of variables we have, the traditional correlation matrix estimation fails to give good results and we need to improve it. In this thesis we used low-rank plus sparse method alternating direction method of multipliers for correlation matrix estimation from the family of Principal component analysis models. Quality of estimation is tested on synthetic data generated via multivariate normal and student’s t-distribution with several ratios of number of data points and variables. We test our method by constructing minimal variance portfolio and compare it with other methods of estimation