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In this paper, we discuss and compare empirically various ways of computing multistep quantile forecasts of demand, with a special emphasis on the use of the quantile regression methodology. Such forecasts constitute a basis for production planning and inventory management in logistics systems optimized according to the cycle service level approach. Different econometric methods and models are considered: direct and iterated computations, linear and nonlinear (GARCH) models, simulation and nonsimulation based procedures and parametric as well as semiparametric specifications. These methods are applied to compute multiperiod quantile forecasts of the monthly microeconomic time series from the popular M3 competition database. According to various accuracy measures for quantile predictions, the best procedures are based on simulation techniques using predictive distributions generated by either the quantile regression methodology combined with random draws from the uniform distribution or parametric and nonparametric bootstrap techniques. These methods lead to large reductions in the total costs of logistics systems as compared with non-simulation based procedures. For example, in the case of forecasting 12 months ahead, relatively short time series and a high cycle service level, the quantile regression based simulation approach reduces the average supply chain cost per unit of output by about 70-85%. At the shortest horizons, the GARCH model should be seriously considered among the preferred forecasting solutions for production and inventory planning.

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In the paper, we undertake a detailed empirical verification of wavelet scaling as a forecasting method through its application to a large set of noisy data. The method consists of two steps. In the first, the data are smoothed with the help of wavelet estimators of stochastic signals based on the idea of scaling, and, in the second, an AR(I)MA model is built on the estimated signal. This procedure is compared with some alternative approaches encompassing exponential smoothing, moving average, AR(I)MA and regularized AR models. Special attention is given to the ways of treating boundary regions in the wavelet signal estimation and to the use of biased, weakly biased and unbiased estimators of the wavelet variance. According to a collection of popular forecast accuracy measures, when applied to noisy time series with a high level of noise, wavelet scaling is able to outperform the other forecasting procedures, although this conclusion applies mainly to longer time series and not uniformly across all the examined accuracy measures.