Multivariate Methods

probability calculus: multivariate distributions with a focus on the bivariate normal distribution, covariance and correlation; estimation of the moments and distributions of linear combinations of random variables. inferential statistics: fundamentals of estimation and desirable properties of estimators (unbiasedness, efficiency and consistency); Maximum Likelihood estimator, estimation of the expected value, proportion, variance, covariance and correlation; foundation of test procedures: structure of tests (Null-hypothesis, test statistic, acceptance or rejection of null hypothesis), type I and type II errors (alpha and beta errors); test for proportion and expected value; structure and assumption of a simple linear regression: estimation of parameters and testing for significance. multivariate regression: estimation of the parameters, goodness-of-fit measures (R2 and adjusted R2) and important tests (t-test and F-test; regression diagnostics); factor models and principal components analysis: introduction with an example from asset and risk management (e.g. forecasting for an equity portfolio); logistic regression: estimation of the parameters, assessing the goodness-of-fit (e.g. ROC- or CAP-curve, Brier-Score), important tests and areas of application in asset or risk management (e.g. for rating models); Neural networks: Estimation of parameters, goodness-of-fit, important tests and areas of application in asset or risk management (e.g. forecasting models for equity or FX)