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In this paper we consider the reduced bootstrap, that consists of only considering those bootstrap samples satisfying k1⩽νn⩽k2, for some 1⩽k1⩽k2⩽n, where νn is the number of distinct original observations in the bootstrap sample. We show that, under mild conditions on k1 and k2, the reduced bootstrap estimator of the distribution of the sample mean is consistent. We also give conditions for it to...
A procedure for designing non-linear models for predicting time series is proposed. It is based on a set of rules emerging from a previously fitted ARIMA model. These rules are extracted from the set of coefficients in the ARIMA model, so they consider the autocorrelation structure of the time series, but a nonlinear approach is adopted. The proposed procedure is intended to help the user in the task...
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