Inference for the Sample Maximum in the Presenceof Serial Correlation and Heavy Tailed Distributions

摘要

We consider data from an infinite order moving average time series modelrnwith inputs in the α-stable domain of attraction, for α ∈ (0, 2): The samplernmaximum of the data is of interest in settings such as insurance andrnfinance; we produce a normalization for this statistic, which, in conjunctionrnwith subsampling methods, will allow for asymptotically correct estimation ofrnits cumulative distribution function. A concrete application to the concept ofrn"safety-first" portfolio selection is given.