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Although the extremes of high-frequency financial transaction data have a huge economic impact,the basic structure of the data has been ignored up to now in this context.Existing time series models were developed for transformed daily financial returns.None of those models was suitable for fitting maxima of intra-day stock returns.This paper proposes nested asymptotic (in)dependent extreme value copulas (Gumbel type and conditional three sectional type)in high dimensional max-stable processes and applies the proposed copulas directly to fitting maxima of intra-day stock returns.