A partially periodic oscillation model combined with heterogeneous autoregression and its application to COVID-19

Abstract

This paper proposes a partially periodic oscillation model, which is motivated by time series modelling for COVID-19 daily confirmed cases, in particular, to represent more accurately the dynamic features of the 7-day periodicity. In order to express the phenomenon of the partial 7-day cycle in the COVID-19 data, some partial periodic part is added to a heterogeneous autoregression model. Estimation algorithm based on the least squares errors and regression analysis is provided and parameter estimation consistency is given along with its proof. A Monte-Carlo simulation study is carried out to investigate the finite-sample performance. The proposed model is applied to the COVID-19 daily confirmed cases of the most affected eight countries which posses the partially periodic oscillation. Model criteria such as RMSE, MAE, HMAE, AIC and BIC are compared with other existing models. Efficiency of the model, relative to the benchmark, is evaluated to reveal its better accuracy performance. Out-of-sample forecasting analysis is conducted as well. The novelty is that this work is a challenging trial to identify the partially periodic oscillation of COVID-19 data, without smoothing, as well as the proposed model outperforms the existing time series models in the empirical analysis of the worldwide COVID-19.