Comparison of ARIMA, ETS, NNAR, TBATS and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy

Abstract

The coronavirus disease (COVID-19) is a severe, ongoing, novel pandemic that emerged in Wuhan, China, in December 2019. As of January 21, 2021, the virus had infected approximately 100 million people, causing over 2 million deaths. This article analyzed several time series forecasting methods to predict the spread of COVID-19 during the pandemic's second wave in Italy (the period after October 13, 2020). The autoregressive moving average (ARIMA) model, innovations state space models for exponential smoothing (ETS), the neural network autoregression (NNAR) model, the trigonometric exponential smoothing state space model with Box-Cox transformation, ARMA errors, and trend and seasonal components (TBATS), and all of their feasible hybrid combinations were employed to forecast the number of patients hospitalized with mild symptoms and the number of patients hospitalized in the intensive care units (ICU). The data for the period February 21, 2020-October 13, 2020 were extracted from the website of the Italian Ministry of Health ( www.salute.gov.it ). The results showed that (i) hybrid models were better at capturing the linear, nonlinear, and seasonal pandemic patterns, significantly outperforming the respective single models for both time series, and (ii) the numbers of COVID-19-related hospitalizations of patients with mild symptoms and in the ICU were projected to increase rapidly from October 2020 to mid-November 2020. According to the estimations, the necessary ordinary and intensive care beds were expected to double in 10 days and to triple in approximately 20 days. These predictions were consistent with the observed trend, demonstrating that hybrid models may facilitate public health authorities' decision-making, especially in the short-term.

Keywords: ARIMA; COVID-19; Hybrid forecasting models; Italy; NNAR; Outbreak; TBATS.

Fig. 1

Patients hospitalized with mild symptoms and in the ICU from February 21, 2020 to October 13, 2020. Source: Italian Ministry of Health [43]

Fig. 2

A neural network with four inputs and an intermediate layer with three hidden neurons

Fig. 3

Models ranked by the MAE and RMSE metrics for patients hospitalized with mild symptoms

Fig. 4

Models ranked by the the MAE and RMSE metrics for patients hospitalized in the ICU

Fig. 5

The six best forecast models for predicting patients with mild symptoms. Notes: the models were ranked (from first to sixth place) on the MAE metric

Fig. 6

The remaining nine forecast models for predicting patients hospitalized with mild symptoms. Notes: The models were ranked (from seventh to fifteenth place) on the MAE metric

Fig. 7

The six best forecast models for predicting patients hospitalized in the ICU. Notes: the models were ranked (from first to sixth place) on the MAE metric

Fig. 8

The remaining nine forecast models for predicting patients hospitalized in the ICU. Notes: the models were ranked (from seventh to fifteenth place) on the MAE metric

Fig. 9

Comparison between forecasts and real data during the period October 14, 2020, to November 12, 2020, for patients hospitalized with mild symptoms (six best models)

Fig. 10

Comparison between forecasts and real data during the period October 14, 2020, to November 12, 2020, for patients hospitalized with mild symptoms (nine remaining models)

Fig. 11

Comparison between forecasts and real data during the period October 14, 2020, to November 12, 2020, for patients hospitalized in the ICU (six best models)

Fig. 12

Comparison between forecasts and real data during the period October 14, 2020, to November 12, 2020, for patients hospitalized in the ICU (nine remaining models)