Modelling intermittent time series and forecasting COVID-19 spread in the USA

Abstract

Forecasting intermittent time series represents a challenging task whose importance increases together with the number of series sporadically observed. However, given the difficulties in modelling the presence of zeros, few methods are available. This article introduces a novel state-space approach defined as Intermittent Local Level (ILL). Our approach allows integrating the intermittent nature of time series and forecasting efficiently. Indeed, the proposed state-space model assumes a Bernoulli dynamics that allows switching between zeros and positive values. Moreover, we derive the unobserved dynamics of the time series and provide a simple method for estimating and forecasting. In addition, our approach allows deriving prediction intervals for intermittent observations.

Finally, we compare our method’s performance with those of standard intermittent models as well as other benchmarks, using the daily number of new cases of COVID-19 observed in nearly 3000 American counties. Predicting the number of newly infected people is important, not only for hospitals but also for policy makers in general. Empirical results show that the suggested approach clearly outperforms the Croston model and its variants when forecasting the number of new Coronavirus cases over a two-week period. In addition, it compares well with non-intermittent benchmarks both in point forecast and prediction intervals.

Keywords:

• Forecasting
• intermittent time series
• state-space modelling
• Croston model
• likelihood evaluation

Acknowledgments

The author wishes to thank two anonymous referees as well as the Editor, John Boylan, for their suggestions and comments to improve the manuscript. In addition, I also wish to thank one of the reviewer and Jane Mackinnon for providing editorial assistance.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 An R file to simulate and check these results is available upon request

2 I am grateful with one anonymous referee who suggested to derive the prediction intervals. Likewise, I am deeply indept with another reviewer who helped me fixing many technical details. Indeed, they both shaped and improved the original manuscript.

3 An alternative, yet equivalent, expression of the variance of z_t is provided in the Appendix.

4 Data are downloadable using this link: https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv

5 It is worth noting, however, that Morlidge (2015) criticised accuracy measures based on absolute errors, in the context of intermittent demand.