Forecasting the COVID-19 epidemic: the case of New Zealand

ABSTRACT

We estimate a statistical model for COVID-19 cases and deaths in New Zealand. New Zealand is an important test case for statistical and theoretical research into the dynamics of the global pandemic since it went through a full cycle of infections. We choose functional forms for infections and deaths that incorporate important features of epidemiological models but allow for flexible parameterization to capture different trajectories of the pandemic. Our Bayesian estimation reveals that the simple statistical framework we employ fits the data well and allows for a transparent characterization of the uncertainty surrounding the trajectories of infections and deaths.

Keywords:

• Bayesian estimation
• forecasting
• COVID-19
• New Zealand

Acknowledgments

James Lee provided exceptional research assistance. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 At the time of writing in the middle of August 2020, an apparently isolated cluster of new infections has appeared in Auckland, with reports of up to 30 new cases. It is not clear as of this point whether this is the start of a ‘second wave’ similar to what has occurred in the U.S.

2 Ho et al. (2020) allow for AR(1) errors in the estimation on U.S. data. For reasons of parsimony, given the small sample available in New Zealand, we impose i.i.d. errors, especially since preliminary estimates did not suggest strong serial correlation

3 Ho et al. (2020) show simulation results that detail how the various model parameters affect and determine the pattern of the infection path.

4 Ho et al. (2020) use a more general mortality function given the wider variability and availability of U.S. data, where mortality depends on testing. Alternatively, the death rate λ could be specified as some function of time. The cycle in New Zealand is very short, however, so that the time trend may not be as important as in the U.S. The somewhat simpler specification that we implement here arguably provides a good enough description, especially given the small number of fatalities in New Zealand.

5 There is likely to be measurement error with a possible undercount in this variable since case numbers depend on the amount of testing. Moreover, it is a priori unclear in which direction the measurement error goes for recorded deaths. This is a general problem that researchers have to confront at this stage of the pandemic. In the case of New Zealand, at least probable and confirmed cases are reported. In principle, this could be addressed by including measurement error in the specification explicitly, but we likely pick up some aspects via the shocks in our model.

6 After May 8 the data record a few numbers in the single digits of additional new cases. However, as the graph shows, and as news reports indicated, the epidemic was largely contained by then. We also estimated the model for data up to August 10; its fit, however, deteriorated markedly, giving an arguably incorrect picture of the path of the epidemic. The underlying reason is that we assume shocks can only scale the number of cases up and down. Consequently, when the model indicates that the epidemic cycle is over, a huge shock is needed to fit any incoming data, even if there are only a small number of new cases. As a result, the estimation likely puts too much weight on these end-of-cycle observations, therefore biasing the inference. These additional results are available from the authors upon request.

7 Our estimated peak of new cases follows the government's introduction of Alert Level 2 on March 21, Alert Level 3 on March 23 and Alert Level 4 on March 25. As Figure 1 shows, the estimated peak is not reflected in the actual data. That is, the model specification provided enough momentum from rising case numbers to impute a higher peak than actually occurred. It is tempting to speculate that this is due to the rapid imposition of alert levels and ever tighter lockdowns. An analysis of the value of lockdowns and social distancing policies is beyond the scope of this paper since it requires a more structural framework or much richer data on social distancing measures than is available for New Zealand.

8 When estimated on data up to March 30, the error bands are extremely wide, ranging from zero to 200,000 total cases. At that point, the cumulative number of infections was barely 700. As discussed above, the high growth rates at the onset of an epidemic are a challenge for modelers and forecasters as predictions can be considerably off since even small parameter uncertainty can lead to large long-run forecast uncertainty. This is especially exacerbated in non-linear environments. Hence, a proper treatment of uncertainty and regular updating of estimates should be of foremost importance.