Econometrics

A time-component is typical for many economic applications. How do returns behave? What happens with specific prices over the years (Big-Mac-Index)? Depending on the field of application the relevant questions might be fairly different. But for statistics most of the problems have a common structure - being time-based. The central problem is always how the data behaves over time.

There is a general class of statistical models - ARIMA and linear-regression-models to name just two examples - to detect relationships between time-series and to make forecasts for specific time series.

Panel data analysis - or longitudinal data analysis - is a common method in social science, epidimiologics and econometrics to analyze two dimensional data. Typically the one dimension is the time, as data is gathered at multiple time points. The other dimension might be different patients, individuals or different companies. Data is collected for all of them at different points in time.

Often panel data analysis is performed as a generalization of simple time series analysis. But there are even more powerful tools that will give more precise results.

Business arithmetics are a discipline of applied mathematics and deal with typical problems of finance and especially banks. Foundation of business arithmetics are for sure the two fundamental propositions of price theory. They help to generate formal answers to two central economic problems.

The field of business arithmetics evolved dramatically in the last 30 years. Classical models like Black/Merton/Scholes or Cox/Ross/Rubinstein were generalized and extended by more flexible models. A particularly useful tool is Monte-Carlo-simulation, allowing to calculate even high-dimensional models.

Actuary science deals with risk evaluations. Risks are analyzed using quantitative mathematical and statistical models. This is highly relevant for every kind of company, as success is always based on risks and dealing with risks in a adequate way. Of course banks and insurances are most relevant for actuary scientists.