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Abstract:
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Consider independent replicates of time series with long-range dependence & long-memory parameters, that are iid bounded random variables on (0,1/2) with an unknown distribution. Let each series be Gaussian subordinated via a monotone transformation, so that the marginal distributions of the transformed processes are non-Gaussian. Examples of time series replicates with long-memory & complex marginal distributions can be found in many fields of research. Suppose that we wish to estimate the common trend function using kernel smoothing. This requires in particular, estimation of the unconditional variance of the trend estimate for optimal bandwidth selection. We outline an algorithm that partly relies on the empirical moment generating function of the estimated long-memory parameters and does not require knowledge of their underlying distribution.
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