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Over the last 15 years, studies on hierarchical forecasting have moved away from single-level approaches towards proposing linear combination approaches across multiple levels of the hierarchy. Such combinations offer coherent reconciled forecasts, improved forecasting performance and aligned decision-making. This paper proposes a novel hierarchical forecasting approach based on machine learning. The proposed method allows for non-linear combinations of the base forecasts, thus being more general than linear approaches. We structurally combine the objectives of improved post-sample empirical forecasting accuracy and coherence. Due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns. • We use machine learning approaches for hierarchical reconciliation. • We offer a non-linear approach to the problem of hierarchical coherence. • Our approach explicitly focuses on post-sample in estimating the combination weights. • Our approach offers improved forecasting performance on two real-life data sets. [ABSTRACT FROM AUTHOR]

Inspired by the successful use of deep learning in computer vision, in this paper we introduce ForCNN , a novel deep learning method for univariate time series forecasting that mixes convolutional and dense layers in a single neural network. Instead of using conventional, numeric representations of time series data as input to the network, the proposed method considers visual representations of it in the form of images to directly produce point forecasts. Three variants of deep convolutional neural networks are examined to process the images, the first based on VGG-19, the second on ResNet-50, while the third on a self-designed architecture. The performance of the proposed approach is evaluated using time series of the M3 and M4 forecasting competitions. Our results suggest that image-based time series forecasting methods can outperform both standard and state-of-the-art forecasting models. • An image-based deep learning method for time series forecasting is proposed. • Numeric time series data are converted to images using simple line plots. • Deep convolutional neural networks are employed for producing forecasts from each image. • The proposed, image-based, method outperforms state-of-the-art forecasting methods. [ABSTRACT FROM AUTHOR]

• Empirical evaluation of data augmentation techniques for univariate time series forecasting. • Data augmentation techniques based on combining or upsampling the original time series improve the forecasting performance of neural networks. • Accuracy improvements from data augmentation are more significant when deeper neural networks are used. • Accuracy improvements from data augmentation become less significant as the initial size of the set increases. Neural networks have been proven particularly accurate in univariate time series forecasting settings, requiring however a significant number of training samples to be effectively trained. In machine learning applications where available data are limited, data augmentation techniques have been successfully used to generate synthetic data that resemble and complement the original train set. Since the potential of data augmentation has been largely neglected in univariate time series forecasting, in this study we investigate nine data augmentation techniques, ranging from simple transformations and adjustments to sophisticated generative models and a novel upsampling approach. We empirically evaluate the impact of data augmentation on forecasting accuracy considering both shallow and deep feed-forward neural networks and time series data sets of different sizes from the M4 and the Tourism competitions. Our results suggest that certain data augmentation techniques that build on upsampling and time series combinations can improve forecasting performance, especially when deep networks are used. However, these improvements become less significant as the initial size of the train set increases. [ABSTRACT FROM AUTHOR]