Abstract:We provide a new approach to automatic forecasting based on an extended range of exponential smoothing methods. Each method in our taxonomy of exponential smoothing methods provides forecasts that are equivalent to forecasts from a state space model. This equivalence allows (1) easy calculation of the likelihood, the AIC and other model selection criteria; (2) computation of prediction intervals for each method; and (3) random simulation from the underlying state space model. We demonstrate the methods by applying them to the data from the M-competition and the M3-competition. The method provides forecast accuracy comparable to the best methods in the competitions; it is particularly good for short forecast horizons with seasonal data.

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semiparametric estimate of the long memory parameter is also explored. Higherorder improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first-and second-order moments, the discrete Fourier transform and regression coefficients.The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid. *

This paper investigates bootstrap-based bias correction of semiparametric estimators of the long memory parameter, d, in fractionally integrated processes. The resampling method involves the application of the sieve bootstrap to data prefiltered by a preliminary semiparametric estimate of the long memory parameter. Theoretical justification for using the bootstrap technique to bias adjust log periodogram and semiparametric local Whittle estimators of the memory parameter is provided in the case where the true value of d lies in the range 0 ≤ d < 0.5. That the bootstrap method provides confidence intervals with the correct asymptotic coverage is also proven, with the intervals shown to adjust explicitly for bias, as estimated via the bootstrap. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias-correction techniques is presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which some degree of bias reduction has already been accomplished by analytical means.

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