Modelling the persistence of Covid-19 positivity rate in Italy

The current Covid-19 pandemic is severely affecting public health and global economies. In this context, accurately predicting its evolution is essential for planning and providing resources effectively. This paper aims at capturing the dynamics of the positivity rate (PPR) of the novel coronavirus using the Heterogeneous Autoregressive (HAR) model. The use of this model is motivated by two main empirical features arising from the analysis of PPR time series: the changing long-run level and the persistent autocorrelation structure. Compared to the most frequently used Autoregressive Integrated Moving Average (ARIMA) models, the HAR is able to reproduce the strong persistence of the data by using components aggregated at different interval sizes, remaining parsimonious and easy to estimate. The relative merits of the proposed approach are assessed by performing a forecasting study on the Italian dataset. As a robustness check, the analysis of the positivity rate is also conducted by considering the case of the United States. The ability of the HAR-type models to predict the PPR at different horizons is evaluated through several loss functions, comparing the results with those generated by ARIMA models. The Model Confidence Set is used to test the significance of differences in the predictive performances of the models under analysis. Our findings suggest that HAR-type models significantly outperform ARIMA specifications in terms of forecasting accuracy. We also find that the PPR could represent an important metric for monitoring the evolution of hospitalizations, as the peak of patients in intensive care units occurs within 12-16 days after the peak in the positivity rate. This can help governments in planning socio-economic and health policies in advance.