期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：2
页码：1105-1128
DOI：10.30757/ALEA.v16-41
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We present a Gaussian process that arises from the iteration of p fractionalOrnstein–Uhlenbeck processes generated by the same fractional Brownianmotion. When the values of the parameters defining the iteration are pairwisedistinct, this iteration results in a particular linear combination of those processes.Although for H > 1=2 each term of the iteration is a long memory process, we provethat when p 2 the process obtained has short memory. We prove that the localHölder index of the process is H, and obtain an explicit formula for the spectraldensity. We present a way to estimate the parameters and prove that the estimatorsare consistent and the results are asymptotically Gaussian. These processes can beused to model time series of long or short memory.
