2019/05/24 by Tareq Alodat, Alodat, Tareq, Andriy Olenko +1
Mathematics · Economics, Econometrics and Finance · #Statistical Methods and Inference #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.1905.10030
The paper studies the asymptotic behaviour of weighted functionals of\nlong-range dependent data over increasing observation windows. Various\nimportant statistics, including sample means, high order moments, occupation\nmeasures can be given by these functionals. It is shown that in the discrete\nsampling case additive functionals have the same asymptotic distribution as the\ncorresponding integral functionals for the continuous functional data case.\nThese results are applied to obtain non-central limit theorems for weighted\nadditive functionals of random fields. As the majority of known results concern\nthe discrete sampling case the developed methodology helps in translating these\nresults to functional data without deriving them again. Numerical studies\nsuggest that the theoretical findings are valid for wider classes of long-range\ndependent data.\n