We show that the power of the KPSS-test against integration, as measured by divergence rates of the test statistic under the alternative, remains the same when residuals from an OLS-regression rather than true observations are used. This is in stark contrast to residual based tests of the null...

When calculating the cost of entering into a credit transaction the predominant stochastic component is the expected loss. Often in the credit business the one-year probability of default of the liable counterpart is the only reliable parameter. We use this probability to calculating the exact...

The aim of this paper is to extract mathematically talented students out of a group of arbitrary high school students. We do this by applying a stepwise discriminant analysis modified for ordinal data to the results of German high school students at the international mathematics competition...

In this paper we compare the price of an option with one year maturity of the German stock index DAX for several volatility models including long memory and leverage effects. We compute the price by applying a present value scheme as well as the Black-Scholes and Hull-White formulas which...

We provide a method for distinguishing long-range dependence from deterministic trends such as structural breaks. The method is based on the comparison of standard log-periodogram regression estimation of the memory parameter with its tapered counterpart. The difference of these estimators...

Markov Chains are introduced by only assuming some knowledge of the notion of probability. The modelling of a situation in a context of biology gives the opportunity to students to approach various concepts of probability theory themselves.

Das Abflussverhalten des Rheins wird mittels flexibler saisonaler Modelle mit langem Gedächtnis modelliert. Zur Schätzung der Persistenz wird für jede Saisonfrequenz separat eine Log-Periodogramm Regression durchgeführt. Verglichen mit Standard-ARMA-Prozessen liefern diese Modelle eine gute...

Cointegration describes the pattern that pairs of time series keep together in long run, although they diverge in short run. A generalisation of this behaviour is the fractional cointegration. Two statistical tests, the M– and ML–test are formulated for fractional cointegration in different...

We show that small trends do not influence log-periodogram based estimators for the memory parameter in a stationary invertible long-memory process. In the case of slowly decaying trends which are easily confused with long-range dependence we show by Monte Carlo methods that the tapered...

We show that there is strong evidence of long-range dependence in the volatilities of several German stock returns. This will be done by estimating the memory parameter of the absolute returns with classical log-periodogram regression as well as by employing the tapered periodogram. Both...