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This paper demonstrates the cases where bootstrap does not work for heteroscedastic time series models. We construct prediction intervals for the ARMA-GARCH models using bootstrap and see how a wrong application of bootstrap could lead to a false conclusion

In a scheme of independent, possibly Type-II censored samples, joint estimation of scale parameters is considered under an order statistics prior leading to strictly ascendingly ordered Bayes estimators. The focus is on deriving handy closed-form expressions for the estimators

In this paper we study the integer-valued autoregressive model, which belongs to the class of thinning models with count data.We mainly focus on the random coefficient integer-valued autoregressive (RCINAR) model and propose a conditional least absolute deviation (CL 1 ) method to estimate the parameters of the model. The asymptotic distribution of the CL 1 estimator is investigated. The finite sample performance of the proposed estimator is evaluated through simulation, and is compared with that of conditional least squares (CL 2 ) estimation method. Simulation results show that the proposed method is effective and robust against outliers

We introduce a class of optimal stopping problems in which the gain is at least a fraction of the initial value. From a financial point of view this structure can be seen as a guarantee for the holder of an American option. It turns out that the optimal strategies are of two-sided type under weak conditions. If the driving process is a diffusion we use harmonic-functions techniques to obtain general results. For an explicit solution we derive two differential equations that characterize the optimal strategies. Furthermore we study the case of Lévy processes. An explicit solution is obtained for spectrally negative processes using scale functions

We investigate time consistency of monetary valuations, also called monetary risk measures or monetary utility functions. Through a number of recent research contributions, it has become clear that time consistency imposes strong constraints on families of monetary valuations conditioned on available information at different time instants. In this paper we add to these results by showing that consistent families of monetary valuations are already determined uniquely by the choice of the initial valuation, under suitable sensitivity assumptions; moreover, this statement holds even when the term “consistency” is interpreted in a rather weak sense. The unique update rule is specified explicitly, and we characterize the existence of consistent updates for a given initial monetary valuation. We give examples of situations in which weak consistency is relevant. An application is given to the construction of consistent families of compound valuations, as an illustration of the additional flexibility under weak time consistency