A note on using the empirical moment generating function to estimate the variance of nonparametric trend estimates from independent time series replicates

摘要

Time series with long-range dependence is often assumed to have been generated from a transformation of a latent stationary Gaussian process with long-memory. Suppose that we have k independent replicates of such time series, which have a common trend g(t). Moreover, each series is long range dependent with long-memory parameters delta(1), ..., delta(k), which are independently and identically distributed random variables on (0, 1/2) having an unknown probability distribution. For nonparametric estimation of g(t), an important problem is estimation of the variance of the trend estimator. In this note, we propose an algorithm that partially relies on the moment generating function of delta(1), ..., delta(k).