  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.
