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...

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.

We derive the limiting null distributions of the standard and OLS based CUSUM-tests for structural change of the coecients of a linear regression model in the context of long memory disturbances. We show that both tests behave fundamentally different in a long memory environment, as compared to...

In this paper we consider the asymptotic distribution of S -estimators in the nonlinear regression model with long-memory error terms. S - estimators are robust estimates with a high breakdown point and good asymptotic properties in the i.i.d case. They are constructed for linear regression. In...

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...

The paper discusses structural change as possible mechanism that generates the appearance of long memory in economic time series. It shows that there are no long memory effects in German stock returns and that long memory in squares of German stock returns disappears once shifting means are...

Prediction in time series models with a trend requires reliable estima- tion of the trend function at the right end of the observed series. Local polynomial smoothing is a suitable tool because boundary corrections are included implicitly. However, outliers may lead to unreliable estimates, if...

We investigate the behavior of nonparametric kernel M-estimators in the presence of long-memory errors. The optimal bandwidth and a central limit theorem are obtained. It turns out that in the Gaussian case all kernel M-estimators have the same limiting normal distribution. The motivation behind...