Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread

The ECMWF Ensemble Prediction System: Looking Back (more than) 25 Years and Projecting Forward 25 Years

This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast system. In particular, the reasons for the development of singular vectors and stochastic physics - particular features of the ECMWF Ensemble Prediction System - are discussed. The author speculates about the development and use of ensemble prediction in the next 25 years.Comment: Submitted to Special Issue of the Quarterly Journal of the Royal Meteorological Society: 25 years of ensemble predictio

Ensemble Sales Forecasting Study in Semiconductor Industry

Sales forecasting plays a prominent role in business planning and business strategy. The value and importance of advance information is a cornerstone of planning activity, and a well-set forecast goal can guide sale-force more efficiently. In this paper CPU sales forecasting of Intel Corporation, a multinational semiconductor industry, was considered. Past sale, future booking, exchange rates, Gross domestic product (GDP) forecasting, seasonality and other indicators were innovatively incorporated into the quantitative modeling. Benefit from the recent advances in computation power and software development, millions of models built upon multiple regressions, time series analysis, random forest and boosting tree were executed in parallel. The models with smaller validation errors were selected to form the ensemble model. To better capture the distinct characteristics, forecasting models were implemented at lead time and lines of business level. The moving windows validation process automatically selected the models which closely represent current market condition. The weekly cadence forecasting schema allowed the model to response effectively to market fluctuation. Generic variable importance analysis was also developed to increase the model interpretability. Rather than assuming fixed distribution, this non-parametric permutation variable importance analysis provided a general framework across methods to evaluate the variable importance. This variable importance framework can further extend to classification problem by modifying the mean absolute percentage error(MAPE) into misclassify error. Please find the demo code at : https://github.com/qx0731/ensemble_forecast_methodsComment: 14 pages, Industrial Conference on Data Mining 2017 (ICDM 2017