This paper argues that the distribution of the coefficients of the regular continued fraction should be considered for each algebraic number of degree 2 separately. For random numbers the coefficients are distributed by the Gauss-Kuzmin distribution (also called Khinchin's law). We apply the...

In ESTAR models it is usually dfficult to determine parameter estimates, as it can be observedin the literature. We show that the phenomena of getting strongly biased estimators is aconsequence of the so-called identication problem, the problem of properly distinguishing thetransition function...

Determining good parameter estimates in ESTAR models is known to be difficult. We showthat the phenomena of getting strongly biased estimators is a consequence of the so-calledidentication problem, the problem of properly distinguishing the transition function in relationto extreme parameter...

This paper analyzes and quantifies the idea of model risk in the environment of internal modelbuilding. We define various types of model risk including estimation risk, model risk in distributionand model risk in functional form. By the quantification of these concepts we analyzethe impact of...

While it is widely agreed that Purchasing Power Parity (PPP) holds as a long-runconcept the specific dynamic driving the process is largely build upon a priori economicbelief rather than a thorough statistical modeling procedure. The two prevailing timeseries models, i.e. the exponential smooth...

We study the empirical behaviour of semi-parametric log-periodogram estimation forlong memory models when the true process exhibits a change in persistence. Simulationresults confirm theoretical arguments which suggest that evidence for long memory islikely to be found...

Als Teil des operationellen Risikos stellt das Modellrisiko eine wichtige Komponente f¨urdie Risikoermittlung bei Finanzinstitutionen dar. Da letztere z.B. bei der Tarifierung undBepreisung von Derivaten bzw. Portfolien oder bei der Markt- und Kreditrisikoberechnungauf stochastische Modelle...

We develop a Wald type test to distinguish between long memory and ESTARnonlinearity by using a directed-Wald statistic to overcome the problem of restricted parametersunder the alternative. The test is derived from two basic model specificationswhere the first is the standard model based on an...

Model risk as part of the operational risk is a serious problem for financial institutions.As the pricing of derivatives as well as the computation of the marketor credit risk of an institution depend on statistical models the application of awrong model can lead to a serious over- or...

We show that tests for a break in the persistence of a time series in the classicalI(0) - I(1) framework have serious size distortions when the actual data generatingprocess exhibits long-range dependencies. We prove that the limiting distributionof a CUSUM of squares based test depends on the...