DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks

Probabilistic forecasting, i.e. estimating the probability distribution of a time series' future given its past, is a key enabler for optimizing business processes. In retail businesses, for example, forecasting demand is crucial for having the right inventory available at the right time at the right place. In this paper we propose DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an auto regressive recurrent network model on a large number of related time series. We demonstrate how by applying deep learning techniques to forecasting, one can overcome many of the challenges faced by widely-used classical approaches to the problem. We show through extensive empirical evaluation on several real-world forecasting data sets accuracy improvements of around 15% compared to state-of-the-art methods.

[1]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[2]  J. Chow,et al.  A hybrid ARIMA and artificial neural networks model to forecast particulate matter in urban areas: The case of Temuco, Chile , 2008 .

[3]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[4]  George Athanasopoulos,et al.  Forecasting: principles and practice , 2013 .

[5]  Alex Graves,et al.  Generating Sequences With Recurrent Neural Networks , 2013, ArXiv.

[6]  A. Solis,et al.  Lumpy demand forecasting using neural networks , 2001, PICMET '01. Portland International Conference on Management of Engineering and Technology. Proceedings Vol.1: Book of Summaries (IEEE Cat. No.01CH37199).

[7]  Philip M. Kaminsky,et al.  Designing and managing the supply chain : concepts, strategies, and case studies , 2007 .

[8]  Matthias W. Seeger,et al.  Bayesian Intermittent Demand Forecasting for Large Inventories , 2016, NIPS.

[9]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[10]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[11]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[12]  Inderjit S. Dhillon,et al.  Temporal Regularized Matrix Factorization for High-dimensional Time Series Prediction , 2016, NIPS.

[13]  Jean-François Toubeau,et al.  Deep Learning-Based Multivariate Probabilistic Forecasting for Short-Term Scheduling in Power Markets , 2019, IEEE Transactions on Power Systems.

[14]  Jürgen Schmidhuber,et al.  Applying LSTM to Time Series Predictable through Time-Window Approaches , 2000, ICANN.

[15]  J. Boylan,et al.  Empirical evidence on individual, group and shrinkage seasonal indices , 2008 .

[16]  R. Fildes,et al.  Measuring forecasting accuracy : the case of judgmental adjustments to SKU-level demand forecasts , 2013 .

[17]  Christos Faloutsos,et al.  Forecasting Big Time Series: Theory and Practice , 2019, KDD.

[18]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[19]  Shih-Chii Liu,et al.  Phased LSTM: Accelerating Recurrent Network Training for Long or Event-based Sequences , 2016, NIPS.

[20]  Heiga Zen,et al.  WaveNet: A Generative Model for Raw Audio , 2016, SSW.

[21]  Chu‐Hua Kuei,et al.  Designing and Managing the Supply Chain Concepts, Strategies, and Case Studies , 2000 .

[22]  Thomas G. Dietterich.  Adaptive computation and machine learning , 1998 .

[23]  David Zimbra,et al.  A dynamic artificial neural network model for forecasting time series events , 2005 .

[24]  Samy Bengio,et al.  Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks , 2015, NIPS.

[25]  Juan R. Trapero,et al.  On the identification of sales forecasting models in the presence of promotions , 2015, J. Oper. Res. Soc..

[26]  J. Ord,et al.  Forecasting the intermittent demand for slow-moving inventories: A modelling approach , 2012 .

[27]  J. D. Croston.  Forecasting and Stock Control for Intermittent Demands , 1972 .

[28]  Matthias W. Seeger,et al.  Deep State Space Models for Time Series Forecasting , 2018, NeurIPS.

[29]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[30]  Rob J. Hyndman,et al.  Optimal combination forecasts for hierarchical time series , 2011, Comput. Stat. Data Anal..

[31]  Luís Torgo,et al.  Ensembles for Time Series Forecasting , 2014, ACML.

[32]  Christoph Bergmeir,et al.  Forecasting Across Time Series Databases using Long Short-Term Memory Networks on Groups of Similar Series , 2017, ArXiv.

[33]  Quoc V. Le,et al.  Sequence to Sequence Learning with Neural Networks , 2014, NIPS.

[34]  Milton S. Boyd,et al.  Designing a neural network for forecasting financial and economic time series , 1996, Neurocomputing.

[35]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[36]  Sven F. Crone,et al.  Forecasting and operational research: a review , 2008, J. Oper. Res. Soc..

[37]  Alex Graves,et al.  DRAW: A Recurrent Neural Network For Image Generation , 2015, ICML.

[38]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[39]  Nicolas Chapados,et al.  Effective Bayesian Modeling of Groups of Related Count Time Series , 2014, ICML.

[40]  Zheng Zhang,et al.  MXNet: A Flexible and Efficient Machine Learning Library for Heterogeneous Distributed Systems , 2015, ArXiv.

[41]  Aris A. Syntetos,et al.  The Application of Product-Group Seasonal Indexes to Individual Products , 2012 .

[42]  John F. MacGregor,et al.  Some Recent Advances in Forecasting and Control , 1968 .

[43]  Evangelos Spiliotis,et al.  The M4 Competition: Results, findings, conclusion and way forward , 2018, International Journal of Forecasting.

[44]  Nikolaos Kourentzes,et al.  Intermittent demand forecasts with neural networks , 2013 .