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Forecast with Forecasts: Diversity Matters

arXiv.org Machine Learning

Forecast combination has been widely applied in the last few decades to improve forecast accuracy. In recent years, the idea of using time series features to construct forecast combination model has flourished in the forecasting area. Although this idea has been proved to be beneficial in several forecast competitions such as the M3 and M4 competitions, it may not be practical in many situations. For example, the task of selecting appropriate features to build forecasting models can be a big challenge for many researchers. Even if there is one acceptable way to define the features, existing features are estimated based on the historical patterns, which are doomed to change in the future, or infeasible in the case of limited historical data. In this work, we suggest a change of focus from the historical data to the produced forecasts to extract features. We calculate the diversity of a pool of models based on the corresponding forecasts as a decisive feature and use meta-learning to construct diversity-based forecast combination models. A rich set of time series are used to evaluate the performance of the proposed method. Experimental results show that our diversity-based forecast combination framework not only simplifies the modelling process but also achieves superior forecasting performance.


A Multi-Phase Approach for Product Hierarchy Forecasting in Supply Chain Management: Application to MonarchFx Inc

arXiv.org Machine Learning

Hierarchical time series demands exist in many industries and are often associated with the product, time frame, or geographic aggregations. Traditionally, these hierarchies have been forecasted using top-down, bottom-up, or middle-out approaches. The question we aim to answer is how to utilize child-level forecasts to improve parent-level forecasts in a hierarchical supply chain. Improved forecasts can be used to considerably reduce logistics costs, especially in e-commerce. We propose a novel multi-phase hierarchical (MPH) approach. Our method involves forecasting each series in the hierarchy independently using machine learning models, then combining all forecasts to allow a second phase model estimation at the parent level. Sales data from MonarchFx Inc. (a logistics solutions provider) is used to evaluate our approach and compare it to bottom-up and top-down methods. Our results demonstrate an 82-90% improvement in forecast accuracy using the proposed approach. Using the proposed method, supply chain planners can derive more accurate forecasting models to exploit the benefit of multivariate data.


Model selection in reconciling hierarchical time series

arXiv.org Machine Learning

Model selection has been proven an effective strategy for improving accuracy in time series forecasting applications. However, when dealing with hierarchical time series, apart from selecting the most appropriate forecasting model, forecasters have also to select a suitable method for reconciling the base forecasts produced for each series to make sure they are coherent. Although some hierarchical forecasting methods like minimum trace are strongly supported both theoretically and empirically for reconciling the base forecasts, there are still circumstances under which they might not produce the most accurate results, being outperformed by other methods. In this paper we propose an approach for dynamically selecting the most appropriate hierarchical forecasting method and succeeding better forecasting accuracy along with coherence. The approach, to be called conditional hierarchical forecasting, is based on Machine Learning classification methods and uses time series features as leading indicators for performing the selection for each hierarchy examined considering a variety of alternatives. Our results suggest that conditional hierarchical forecasting leads to significantly more accurate forecasts than standard approaches, especially at lower hierarchical levels.


Forecasting reconciliation with a top-down alignment of independent level forecasts

arXiv.org Machine Learning

Hierarchical forecasting with intermittent time series is a challenge in both research and empirical studies. The overall forecasting performance is heavily affected by the forecasting accuracy of intermittent time series at bottom levels. In this paper, we present a forecasting reconciliation approach that treats the bottom level forecast as latent to ensure higher forecasting accuracy on the upper levels of the hierarchy. We employ a pure deep learning forecasting approach N-BEATS for continuous time series on top levels and a widely used tree-based algorithm LightGBM for the bottom level intermittent time series. The hierarchical forecasting with alignment approach is simple and straightforward to implement in practice. It sheds light on an orthogonal direction for forecasting reconciliation. When there is difficulty finding an optimal reconciliation, allowing suboptimal forecasts at a lower level could retain a high overall performance. The approach in this empirical study was developed by the first author during the M5 Forecasting Accuracy competition ranking second place. The approach is business orientated and could be beneficial for business strategic planning.


A Strong Baseline for Weekly Time Series Forecasting

arXiv.org Artificial Intelligence

Many businesses and industries require accurate forecasts for weekly time series nowadays. The forecasting literature however does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method that can be used as a strong baseline in this domain, leveraging state-of-the-art forecasting techniques, forecast combination, and global modelling. Our approach uses four base forecasting models specifically suitable for forecasting weekly data: a global Recurrent Neural Network model, Theta, Trigonometric Box-Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA). Those are then optimally combined using a lasso regression stacking approach. We evaluate the performance of our method against a set of state-of-the-art weekly forecasting models on six datasets. Across four evaluation metrics, we show that our method consistently outperforms the benchmark methods by a considerable margin with statistical significance. In particular, our model can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset.