Deep learning based forecasting methods have become the methods of choice in many applications of time series prediction or forecasting often outperforming other approaches. Consequently, over the last years, these methods are now ubiquitous in large-scale industrial forecasting applications and have consistently ranked among the best entries in forecasting competitions (e.g., M4 and M5). This practical success has further increased the academic interest to understand and improve deep forecasting methods. In this article we provide an introduction and overview of the field: We present important building blocks for deep forecasting in some depth; using these building blocks, we then survey the breadth of the recent deep forecasting literature.

This paper presents non-parametric baseline models for time series forecasting. Unlike classical forecasting models, the proposed approach does not assume any parametric form for the predictive distribution and instead generates predictions by sampling from the empirical distribution according to a tunable strategy. By virtue of this, the model is always able to produce reasonable forecasts (i.e., predictions within the observed data range) without fail unlike classical models that suffer from numerical stability on some data distributions. Moreover, we develop a global version of the proposed method that automatically learns the sampling strategy by exploiting the information across multiple related time series. The empirical evaluation shows that the proposed methods have reasonable and consistent performance across all datasets, proving them to be strong baselines to be considered in one's forecasting toolbox.

Modern time series corpora, in particular those coming from sensor-based data, exhibit characteristics that have so far not been adequately addressed in the literature on representation learning for time series. In particular, such corpora often allow to distinguish between \emph{exogenous} signals that describe a context which influences a given appliance and \emph{endogenous} signals that describe the internal state of the appliance. We propose a temporal convolution network based embedding that improves on the state-of-the-art by incorporating recent advances in contrastive learning to the time series domain and by adopting a multi-resolution approach. Employing techniques borrowed from domain-adversarial learning, we achieve an invariance of the embeddings with respect to the context provided by the exogenous signal. To show the effectiveness of our approach, we contribute new data sets to the research community and use both new as well as existing data sets to empirically verify that we can separate normal from abnormal internal appliance behaviour independent of the external signals in data sets from IoT and DevOps.

We introduce a novel, practically relevant variation of the anomaly detection problem in multi-variate time series: intrinsic anomaly detection. It appears in diverse practical scenarios ranging from DevOps to IoT, where we want to recognize failures of a system that operates under the influence of a surrounding environment. Intrinsic anomalies are changes in the functional dependency structure between time series that represent an environment and time series that represent the internal state of a system that is placed in said environment. We formalize this problem, provide under-studied public and new purpose-built data sets for it, and present methods that handle intrinsic anomaly detection. These address the short-coming of existing anomaly detection methods that cannot differentiate between expected changes in the system's state and unexpected ones, i.e., changes in the system that deviate from the environment's influence. Our most promising approach is fully unsupervised and combines adversarial learning and time series representation learning, thereby addressing problems such as label sparsity and subjectivity, while allowing to navigate and improve notoriously problematic anomaly detection data sets.

Research on time series forecasting has predominantly focused on developing methods that improve accuracy. However, other criteria such as training time or latency are critical in many real-world applications. We therefore address the question of how to choose an appropriate forecasting model for a given dataset among the plethora of available forecasting methods when accuracy is only one of many criteria. For this, our contributions are two-fold. First, we present a comprehensive benchmark, evaluating 7 classical and 6 deep learning forecasting methods on 44 heterogeneous, publicly available datasets. The benchmark code is open-sourced along with evaluations and forecasts for all methods. These evaluations enable us to answer open questions such as the amount of data required for deep learning models to outperform classical ones. Second, we leverage the benchmark evaluations to learn good defaults that consider multiple objectives such as accuracy and latency. By learning a mapping from forecasting models to performance metrics, we show that our method PARETOSELECT is able to accurately select models from the Pareto front -- alleviating the need to train or evaluate many forecasting models for model selection. To the best of our knowledge, PARETOSELECT constitutes the first method to learn default models in a multi-objective setting.

We introduce Neural Contextual Anomaly Detection (NCAD), a framework for anomaly detection on time series that scales seamlessly from the unsupervised to supervised setting, and is applicable to both univariate and multivariate time series. This is achieved by combining recent developments in representation learning for multivariate time series, with techniques for deep anomaly detection originally developed for computer vision that we tailor to the time series setting. Our window-based approach facilitates learning the boundary between normal and anomalous classes by injecting generic synthetic anomalies into the available data. NCAD can effectively take advantage of domain knowledge and of any available training labels. We demonstrate empirically on standard benchmark datasets that our approach obtains a state-of-the-art performance in the supervised, semi-supervised, and unsupervised settings.

While classical time series forecasting considers individual time series in isolation, recent advances based on deep learning showed that jointly learning from a large pool of related time series can boost the forecasting accuracy. However, the accuracy of these methods suffers greatly when modeling out-of-sample time series, significantly limiting their applicability compared to classical forecasting methods. To bridge this gap, we adopt a meta-learning view of the time series forecasting problem. We introduce a novel forecasting method, called Meta GlobalLocal Auto-Regression (Meta-GLAR), that adapts to each time series by learning in closed-form the mapping from the representations produced by a recurrent neural network (RNN) to one-step-ahead forecasts. Crucially, the parameters of the RNN are learned across multiple time series by backpropagating through the closed-form adaptation mechanism. In our extensive empirical evaluation we show that our method is competitive with the state-of-the-art in out-of-sample forecasting accuracy reported in earlier work.

Realistic synthetic time series data of sufficient length enables practical applications in time series modeling tasks, such as forecasting, but remains a challenge. In this paper we present PSA-GAN, a generative adversarial network (GAN) that generates long time series samples of high quality using progressive growing of GANs and self-attention. We show that PSA-GAN can be used to reduce the error in two downstream forecasting tasks over baselines that only use real data. We also introduce a Frechet-Inception Distance-like score, Context-FID, assessing the quality of synthetic time series samples. In our downstream tasks, we find that the lowest scoring models correspond to the best-performing ones. Therefore, Context-FID could be a useful tool to develop time series GAN models.

Probabilistic forecasting, i.e., estimating a time series’ future probability distribution given its past, is a key enabler for optimizing business processes. In retail businesses, for example, probabilistic demand forecasts are crucial for having the right inventory available at the right time and in the right place. This paper proposes DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an autoregressive recurrent neural network model on a large number of related time series. We demonstrate how the application of deep learning techniques to forecasting can overcome many of the challenges that are faced by widely-used classical approaches to the problem. By means of extensive empirical evaluations on several real-world forecasting datasets, we show that our methodology produces more accurate forecasts than other state-of-the-art methods, while requiring minimal manual work.

We introduce Gluon Time Series (GluonTS, available at https://gluon-ts.mxnet.io), a library for deep-learning-based time series modeling. GluonTS simplifies the development of and experimentation with time series models for common tasks such as forecasting or anomaly detection. It provides all necessary components and tools that scientists need for quickly building new models, for efficiently running and analyzing experiments and for evaluating model accuracy.

There is a large body of research on scalable machine learning (ML). Nevertheless, training ML models on large, continuously evolving datasets is still a difficult and costly undertaking for many companies and institutions. We discuss such challenges and derive requirements for an industrial-scale ML platform. Next, we describe the computational model behind Amazon SageMaker, which is designed to meet such challenges. SageMaker is an ML platform provided as part of Amazon Web Services (AWS), and supports incremental training, resumable and elastic learning as well as automatic hyperparameter optimization. We detail how to adapt several popular ML algorithms to its computational model. Finally, we present an experimental evaluation on large datasets, comparing SageMaker to several scalable, JVM-based implementations of ML algorithms, which we significantly outperform with regard to computation time and cost.

We propose a simple yet effective policy for the predictive auto-scaling of horizontally scalable applications running in cloud environments, where compute resources can only be added with a delay, and where the deployment throughput is limited. Our policy uses a probabilistic forecast of the workload to make scaling decisions dependent on the risk aversion of the application owner. We show in our experiments using real-world and synthetic data that this policy compares favorably to mathematically more sophisticated approaches as well as to simple benchmark policies.

Time series forecasting is a key ingredient in the automation and optimization of business processes: in retail, deciding which products to order and where to store them depends on the forecasts of future demand in different regions; in cloud computing, the estimated future usage of services and infrastructure components guides capacity planning; and workforce scheduling in warehouses and factories requires forecasts of the future workload. Recent years have witnessed a paradigm shift in forecasting techniques and applications, from computer-assisted model- and assumption-based to data-driven and fully-automated. This shift can be attributed to the availability of large, rich, and diverse time series data sources and result in a set of challenges that need to be addressed such as the following. How can we build statistical models to efficiently and effectively learn to forecast from large and diverse data sources? How can we leverage the statistical power of "similar" time series to improve forecasts in the case of limited observations? What are the implications for building forecasting systems that can handle large data volumes? The objective of this tutorial is to provide a concise and intuitive overview of the most important methods and tools available for solving large-scale forecasting problems. We review the state of the art in both: (1) classical modeling of time series, (2) deep learning for forecasting. We also discuss the practical aspects of building a large scale forecasting system, including data integration, feature generation, backtesting framework, error tracking and analysis, etc. Accompanied with the practice side is a hands-on session, where we would engage the audience with Jupyter notebooks that demonstrates the key concepts in the theory part. Furthermore, we provides interactive demos, showing various avenues to solve business problems with AWS Forecasting offerings such as GluonTS, DeepAR (SageMaker), and Amazon Forecast.

Neural network based forecasting methods have become ubiquitous in large-scale industrial forecasting applications over the last years. As the prevalence of neural network based solutions among the best entries in the recent M4 competition shows, the recent popularity of neural forecasting methods is not limited to industry and has also reached academia. This article aims at providing an introduction and an overview of some of the advances that have permitted the resurgence of neural networks in machine learning. Building on these foundations, the article then gives an overview of the recent literature on neural networks for forecasting and applications.

Classifying forecasting methods as being either of a “machine learning” or “statistical” nature has become commonplace in parts of the forecasting literature and community, as exemplified by the M4 competition and the conclusion drawn by the organizers. We argue that this distinction does not stem from fundamental differences in the methods assigned to either class. Instead, this distinction is probably of a tribal nature, which limits the insights into the appropriateness and effectiveness of different forecasting methods. We provide alternative characteristics of forecasting methods which, in our view, allow to draw meaningful conclusions. Further, we discuss areas of forecasting which could benefit most from cross-pollination between the ML and the statistics communities.

Time series modeling techniques based on deep learning have seen many advancements in recent years, especially in data-abundant settings and with the central aim of learning global models that can extract patterns across multiple time series. While the crucial importance of appropriate data pre-processing and scaling has often been noted in prior work, most studies focus on improving model architectures. In this paper we empirically investigate the effect of data input and output transformations on the predictive performance of several neural forecasting architectures. In particular, we investigate the effectiveness of several forms of data binning, i.e. converting real-valued time series into categorical ones, when combined with feed-forward, recurrent neural networks, and convolution-based sequence models. In many non-forecasting applications where these models have been very successful, the model inputs and outputs are categorical (e.g. words from a fixed vocabulary in natural language processing applications or quantized pixel color intensities in computer vision). For forecasting applications, where the time series are typically real-valued, various ad-hoc data transformations have been proposed, but have not been systematically compared. To remedy this, we evaluate the forecasting accuracy of instances of the aforementioned model classes when combined with different types of data scaling and binning. We find that binning almost always improves performance (compared to using normalized real-valued inputs), but that the particular type of binning chosen is of lesser importance.

In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention. We empirically demonstrate the effectiveness of the approach on synthetic and real-world data sets.

We introduce GluonTS, the Gluon Time Series Toolkit, a library for deep learning based time series modeling. GluonTS simplifies the development of and experimentation with time series models for common tasks such as forecasting or anomaly detection. It provides all necessary components and tools that scientists need for quickly building new models, for efficiently running and analyzing experiments and for evaluating model accuracy.

We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target statistics. Inference is approximated by the Newton-Raphson algorithm, reduced to linear-time Kalman smoothing, which allows us to operate on several orders of magnitude larger problems than previous related work. In a study on large real-world sales datasets, our method outperforms competing approaches on fast and medium moving items.

We present a platform built on large-scale, data-centric machine learning (ML) approaches, whose particular focus is demand forecasting in retail. At its core, this platform enables the training and application of probabilistic demand forecasting models, and provides convenient abstractions and support functionality for forecasting problems. The platform comprises of a complex end-to-end machine learning system built on Apache Spark, which includes data preprocessing, feature engineering, distributed learning, as well as evaluation, experimentation and ensembling. Furthermore, it meets the demands of a production system and scales to large catalogues containing millions of items. We describe the challenges of building such a platform and discuss our design decisions. We detail aspects on several levels of the system, such as a set of general distributed learning schemes, our machinery for ensembling predictions, and a high-level dataflow abstraction for modeling complex ML pipelines. To the best of our knowledge, we are not aware of prior work on real-world demand forecasting systems which rivals our approach in terms of scalability.