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The authors deal with forecasting nonstationary time series using wavelets and kernel smoothing. Starting from a basic forecasting procedure based on the regression of the process on the nondecimated Haar wavelet coefficients of the past, the procedure was extended in various directions, including the use of an arbitrary wavelet or polynomial fitting for extrapolating low-frequency components. The authors study a further generalization of the prediction procedure dealing with multistep forecasting and combining kernel smoothing and wavelets. They finally illustrate the proposed procedure on nonstationary simulated and real data and then compare it to well-known competitors. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we are interested in the statistical forecasting of the daily mean PM10 concentration. Hourly concentrations of PM10 have been measured in the city of Rouen, in Haute-Normandie, France. Located at northwest of Paris, near the south side of Manche sea and heavily industrialised. We consider three monitoring stations reflecting the diversity of situations: an urban background station, a traffic station and an industrial station near the cereal harbour of Rouen. We have focused our attention on data for the months that register higher values, from December to March, on years 2004–2009. The models are obtained from the winter days of the four seasons 2004/2005 to 2007/2008 (training data) and then the forecasting performance is evaluated on the winter days of the season 2008/2009 (test data). We show that it is possible to accurately forecast the daily mean concentration by fitting a function of meteorological predictors and the average concentration measured on the previous day. The values of observed meteorological variables are used for fitting the models and are also considered for the test data. We have compared the forecasts produced by three different methods: persistence, generalized additive nonlinear models and clusterwise linear regression models. This last method gives very impressive results and the end of the paper tries to analyze the reasons of such a good behavior. [Copyright &y& Elsevier]

This paper deals with wavelets in time series, focusing on statistical forecasting purposes. Recent approaches involve wavelet decompositions in order to handle non-stationary time series in such context. A method, proposed by Renaud et al.,11 estimates directly the prediction equation by direct regression of the process on the Haar non-decimated wavelet coefficients depending on its past values. In this paper, this method is studied and extended in various directions. The new variants are used first for stationary data and after for stationary data contaminated by a deterministic trend. [ABSTRACT FROM AUTHOR]

Forecasting PM10 concentrations accurately will all for improved early warning procedures, useful for safety reasons and opens for example the possibility to restrict circulation or to decide free public transportation. So the need of a statistical pollution forecasting tool from particulate matter is an important issue for the public authorities. Hourly concentrations of PM10 have been measured in three cities of Haute-Normandie (France): Rouen, Le Havre and Dieppe. The Haute-Normandie region is located at northwest of Paris, near the south side of Manche sea and is heavily industrialized. We consider six monitoring stations reflecting the diversity of situations. We have focused our attention on recent data from 2007 to 2011. We forecast the daily mean PM10 concentration by modeling it as a mixture of linear regression models involving meteorological predictors and the average concentration measured on the previous day. The values of observed meteorological variables are used for fitting the models while the corresponding predictions are considered for the test data, leading to realistic evaluations of forecasting performances, which are calculated through a leave-one-out scheme on the four years. We discuss in this paper several methodological issues including estimation schemes, introduction of the deterministic predictions of meteorological models and how to handle the forecasting at various horizons from some hours to one day ahead. [ABSTRACT FROM AUTHOR]

Smart grids require flexible data driven forecasting methods. We propose clustering tools for bottom-up short-term load forecasting. We focus on individual consumption data analysis which plays a major role for energy management and electricity load forecasting. The first section is dedicated to the industrial context and a review of individual electrical data analysis. Then, we focus on hierarchical time-series for bottom-up forecasting. The idea is to decompose the global signal and obtain disaggregated forecasts in such a way that their sum enhances the prediction. This is done in three steps: identify a rather large number of super-consumers by clustering their energy profiles, generate a hierarchy of nested partitions and choose the one that minimize a prediction criterion. Using a nonparametric model to handle forecasting, and wavelets to define various notions of similarity between load curves, this disaggregation strategy gives a 16% improvement in forecasting accuracy when applied to French individual consumers. Then, this strategy is implemented using R—the free software environment for statistical computing—so that it can scale when dealing with massive datasets. The proposed solution is to make the algorithm scalable combine data storage, parallel computing and double clustering step to define the super-consumers. The resulting software is openly available. [ABSTRACT FROM AUTHOR]