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.

No Change of Pneumocystis jirovecii Pneumonia after the COVID-19 Pandemic: Multicenter Time-Series Analyses

“…We applied the index date for the annual traditional and Bayesian structural timeseries (BSTS) analyses to forecast the PCP cases in the post-COVID-19 period with the observed data (average of PCP cases per month in each year) from the pre-COVID-19 period and compare the monthly average number of forecasted and observed cases in the post-COVID-19 period. For the traditional time-series analyses, the exponential smoothing (ETS) and autoregressive integrated moving average (ARIMA) model for interrupted timeseries analysis were performed using the Python programming language (version 3.9.6) with the Pandas library (version 1.3.0) and statsmodels package (version 0.12.2) [58,59]. The seasonal decomposition in the EST model by multiplicative error assumption was performed to obtain the trends of PCP-suspected and confirmed inpatients and PCP rates with quarterly or yearly frequency [59].…”

“…For the traditional time-series analyses, the exponential smoothing (ETS) and autoregressive integrated moving average (ARIMA) model for interrupted timeseries analysis were performed using the Python programming language (version 3.9.6) with the Pandas library (version 1.3.0) and statsmodels package (version 0.12.2) [58,59]. The seasonal decomposition in the EST model by multiplicative error assumption was performed to obtain the trends of PCP-suspected and confirmed inpatients and PCP rates with quarterly or yearly frequency [59]. The residuals indicating the difference between the forecasted and observed data in the ARIMA model were expressed as estimates (standard error) (%).…”

“…As our time-series data showed stationary characteristics without seasonality, which means that the mean, variance, and covariance of data were invariant to time, in the augmented Dickey-Fuller test (p < 0.001) [66], we applied the non-seasonal ARIMA (1, 0, 1) model using the following parameters, with the lowest Akaike Information Criterion value (388. As our time-series data showed stationary characteristics without seasonality, which means that the mean, variance, and covariance of data were invariant to time, in the augmented Dickey-Fuller test (p < 0.001) [66], we applied the non-seasonal ARIMA (1, 0, 1) model using the following parameters, with the lowest Akaike Information Criterion value (388.7): (1) 1 of autoregression (p) from the autocorrelation function of residuals, (2) 0 of degree of differencing (integrated, d), and (3) 1 of size of the moving average window (q) from the partial autocorrelation function of residuals (Supplementary Figure S3) [59,67,68]. As the observed PCP-confirmed cases did not exist for several months, and average numbers of observed PCP-confirmed cases per month in each year were very small in the pre-and post-COVID-19 periods, we did not perform the time-series analysis for HSCT recipients, chronic lung disease, and HIV-1-infected individuals in the ARIMA and BSTS model.…”

Forecasting of Milk Production in Northern Thailand Using Seasonal Autoregressive Integrated Moving Average, Error Trend Seasonality, and Hybrid Models

“…With the validation dataset, error matrices that were commonly used including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percent error (MAPE) were calculated to determine forecast performances among the developed models ( 26 , 52 ). It is generally accepted that the lower the measure error matric values, the better the method ( 33 ).…”

Comparison of ARIMA, ES, GRNN and ARIMA–GRNN hybrid models to forecast the second wave of COVID-19 in India and the United States

“…Epidemiological time series forecasting plays an important role in disease surveillance, because it allows the managers to develop strategic planning, which helps to avoid a large scale of the epidemic [5]. At present, many mathematical models, including regression analysis method, time series analysis method, and neural network technology, have been applied to predict the incidence of infectious diseases [6][7][8][9]. The autoregressive integrated moving average (ARIMA) model is a time series analysis method firstly proposed by Box and Jenkins in the 1970s, which works based on linear theory; the model mainly captures a linear relationship and assumes the normality of errors [10].…”