Sensitivity analysis of error-contaminated time series data under autoregressive models with the application of COVID-19 data

Abstract

Autoregressive (AR) models are useful in time series analysis. Inferences under such models are distorted in the presence of measurement error, a common feature in applications. In this article, we establish analytical results for quantifying the biases of the parameter estimation in AR models if the measurement error effects are neglected. We consider two measurement error models to describe different data contamination scenarios. We propose an estimating equation approach to estimate the AR model parameters with measurement error effects accounted for. We further discuss forecasting using the proposed method. Our work is inspired by COVID-19 data, which are error-contaminated due to multiple reasons including those related to asymptomatic cases and varying incubation periods. We implement the proposed method by conducting sensitivity analyses and forecasting the fatality rate of COVID-19 over time for the four most populated provinces in Canada. The results suggest that incorporating or not incorporating measurement error effects may yield rather different results for parameter estimation and forecasting.

Keywords:

• Autoregressive model
• COVID-19
• forecasting
• measurement error
• sensitivity analysis
• time series

Acknowledgments

The authors thank the review team for the comments on the initial submission. This research is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Rapid Response Program-COVID-19 of the Canadian Statistical Sciences Institute (CANSSI). Yi is Canada Research Chair in Data Science (Tier 1). Her research was undertaken, in part, thanks to funding from the Canada Research Chairs Program.

Disclosure statement

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

Data availability

All codes and data involved in this paper are available on Github (https://github.com/QihuangZhang/COVID-AR-Error). Preprint available at Zhang and Yi [21].

Additional information

Funding

This research is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Rapid Response Program-COVID-19 of the Canadian Statistical Sciences Institute (CANSSI). Yi is Canada Research Chair in Data Science (Tier 1). Her research was undertaken, in part, thanks to funding from the Canada Research Chairs in Sexual and Gender Minority Health Program.