Rounding errors in autoregressive processes

Time series observations are often rounded, but are modelled as though they were continuous and no rounding had occurred. This paper examines the impact of rounding on the estimation of parameters in autoregressive time series models, deriving appropriate adjustments for the estimates of the true parameters when using rounded data. Analytical results are presented for the asymptotic case, and simulation results are reported for the case of moderate sample sizes. The adjustments are simple and easily implemented, and do not require additional parameter estimation beyond the usual maximum likelihood analysis. Based on the findings of the present analysis, the paper offers specific recommendations on how to adjust the parameter estimates in practice for different levels of rounding.