Copula Models of COVID-19 Mortality in Minnesota and Wisconsin

Abstract

In this study, we assess COVID-19-related mortality in Minnesota and Wisconsin with the aim of demonstrating both the temporal dynamics and the magnitude of the pandemic’s influence from an actuarial risk standpoint. In the initial segment of this paper, we discuss the methodology successfully applied to describe associations in financial and engineering time series. By applying time series analysis, specifically the autoregressive integrated with moving average methods (ARIMA), to weekly mortality figures at the national or state level, we subsequently delve into a marginal distribution examination of ARIMA residuals, addressing any deviation from the standard normality assumption. Thereafter, copulas are utilized to architect joint distribution models across varied geographical domains. The objective of this research is to offer a robust statistical model that utilizes observed mortality datasets from neighboring states and nations to facilitate precise short-term mortality projections. In the subsequent section, our focus shifts to a detailed scrutiny of the statistical interdependencies manifesting between Minnesota and Wisconsin’s weekly COVID-19 mortality figures, adjusted for the time series structure. Leveraging open-source data made available by the CDC and pertinent U.S. state government entities, we apply the ARIMA methodology with subsequent residual distribution modeling. To establish dependence patterns between the states, pair copulas are employed to articulate the relationships between the ARIMA residuals, drawing from fully parametric models. We explore several classes of copulas, comprising both elliptic and Archimedean families. Emphasis is placed on copula model selection. Student t-copula with the marginals modeled by non-standard t-distribution is suggested for ARIMA residuals of Minnesota and Wisconsin COVID mortality as the model of choice based on information criteria and tail cumulation. The copula approach is suggested for the construction of short-term prediction intervals for COVID-19 mortality based on publicly available data.

Keywords

• COVID-19
• mortality
• time series (ARIMA) models
• copula models
• elliptic copulas
• Archimedean family