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 variablesinferential 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 significancemultivariate 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)

Mode of delivery

face to face



Recommended or required reading and other learning resources/tools

Alexander, C., 2008, Practical Financial Econometrics, Wiley & Sons; Brockwell, P., Davis, R., 2006, Time Series: Theory and Methods, 2nd ed., Springer; Brockwell, P., Davis, R., 2010, Introduction to Time Series and Forecasting, 8th ed., Springer; Franses, P., van Dijk, D., 2000, Nonlinear time series models in empirical finance, Cambridge University Press; Shumway, R., Stoffer, D., 2010, Time Series Analysis and its Applications, 3rd ed., Springer; Taylor, S., 2005, Asset Price Dynamics, Volatility, and Prediction, University Press of CA; Tsay, R., 2010, Analysis of Financial Time Series, 3rd ed., John Wiley

Planned learning activities and teaching methods

integrated class

Assessment methods and criteria

Students are assessed on the quality of their assignments, their presentations, their participation and the results of the written quizzes.

Prerequisites and co-requisites

Courses 1 - 4


Degree programme

Quantitative Asset and Risk Management (Master)



ECTS Credits


Language of instruction




Academic year



1 WS



Learning outcome

After the successful completion of the course students are able to interpret and evaluate parameter estimates and goodness-of-fit measures of statistical models (e.g. regression models) in detail and they can judge the accuracy of these models. As the statistical concepts are always taught on the basis of practical examples, the students know in which areas of asset and risk management these advanced multivariate models are used: return distributions and risks of portfolios of assets, models to estimate the default probability of obligors etc.

Course code