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. 2021 Dec;10(1):e369.
doi: 10.1002/sta4.369. Epub 2021 Mar 31.

Count-valued time series models for COVID-19 daily death dynamics

William R Palmer  1 , Richard A Davis  1 , Tian Zheng  1
Affiliations

Count-valued time series models for COVID-19 daily death dynamics

William R Palmer et al. Stat (Int Stat Inst). 2021 Dec.

Abstract

We propose a generalized non-linear state-space model for count-valued time series of COVID-19 fatalities. To capture the dynamic changes in daily COVID-19 death counts, we specify a latent state process that involves second-order differencing and an AR(1)-ARCH(1) model. These modelling choices are motivated by the application and validated by model assessment. We consider and fit a progression of Bayesian hierarchical models under this general framework. Using COVID-19 daily death counts from New York City's five boroughs, we evaluate and compare the considered models through predictive model assessment. Our findings justify the elements included in the proposed model. The proposed model is further applied to time series of COVID-19 deaths from the four most populous counties in Texas. These model fits illuminate dynamics associated with multiple dynamic phases and show the applicability of the framework to localities beyond New York City.

Keywords: Bayesian estimation; COVID‐19 modelling; count‐valued time series; state‐space models.

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Figures

FIGURE 1
FIGURE 1
One hundred days of New York City COVID‐19 mortality data. The observed peak is indicated in red
FIGURE 2
FIGURE 2
Daily COVID‐19 deaths in Queens along with estimates of underlying means λ t . Red shaded regions correspond to out‐of‐sample forecasts. Estimates vary by model and the length of training series (T)
FIGURE 3
FIGURE 3
Estimates of δ t , the second‐order difference of the logarithm of the underlying mean. Red shaded regions correspond to out‐of‐sample forecasts. Estimates vary by model and the length of training series (T)
FIGURE 4
FIGURE 4
Nonrandomized PIT histograms for 1‐day ahead predictive distributions
FIGURE 5
FIGURE 5
Estimates of λ t from the collection of NB(ρ, α 1) model fits. The red shaded regions show out‐of‐sample posterior predictive forecasting. The points are observed actual deaths
FIGURE 6
FIGURE 6
Estimates of δ t from the collection of NB(ρ, α 1) model fits. The red shaded regions show out‐of‐sample posterior predictive forecasting
FIGURE 7
FIGURE 7
PIT histograms for k‐day ahead predictive distributions, for the NB(ρ, α 1) model
FIGURE 8
FIGURE 8
Posterior estimates of λ t and δ t from NB(ρ, α 1) fits to fatality data from the four largest Texas counties
See this image and copyright information in PMC

References

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