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Hybrid methods have been shown to outperform pure statistical and pure deeplearning methods at forecasting tasks and quantifying the associateduncertainty with those forecasts (prediction intervals). One example isExponential Smoothing Recurrent Neural Network (ES-RNN), a hybrid between astatistical forecasting model and a recurrent neural network variant. ES-RNNachieves a 9.4\% improvement in absolute error in the Makridakis-4 ForecastingCompetition. This improvement and similar outperformance from other hybridmodels have primarily been demonstrated only on univariate datasets.Difficulties with applying hybrid forecast methods to multivariate data include($i$) the high computational cost involved in hyperparameter tuning for modelsthat are not parsimonious, ($ii$) challenges associated with auto-correlationinherent in the data, as well as ($iii$) complex dependency (cross-correlation)between the covariates that may be hard to capture. This paper presentsMultivariate Exponential Smoothing Long Short Term Memory (MES-LSTM), ageneralized multivariate extension to ES-RNN, that overcomes these challenges.MES-LSTM utilizes a vectorized implementation. We test MES-LSTM on severalaggregated coronavirus disease of 2019 (COVID-19) morbidity datasets and findour hybrid approach shows consistent, significant improvement over purestatistical and deep learning methods at forecast accuracy and predictioninterval construction.

A Statistics and Deep Learning Hybrid Method for Multivariate Time Series Forecasting and Mortality Modeling