Sensitivity Analysis of Error-Contaminated Time Series Data under Autoregressive Models with Application of COVID-19 Data

TL;DR

This paper analyzes how measurement errors affect autoregressive model estimates in time series data, especially COVID-19 data, proposing methods to account for errors and improve forecasting accuracy.

Contribution

It introduces analytical bias quantification, two measurement error models, and an estimation approach for AR models with error effects, applied to COVID-19 mortality data.

Findings

Neglecting measurement errors biases parameter estimates.

Incorporating error effects significantly alters forecasting results.

The proposed method improves COVID-19 mortality rate predictions.

Abstract

Autoregressive (AR) models are useful tools in time series analysis. Inferences under such models are distorted in the presence of measurement error, which is very common in practice. 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 propose two measurement error models to describe different processes of data contamination. An estimating equation approach is proposed for the estimation of the 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 the asymptomatic cases and varying incubation periods. We implement our proposed method by conducting sensitivity analyses and forecasting of the mortality 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 yields rather different results for parameter estimation and forecasting.