Incomplete Angular Time Series Imputation with a Projected Normal Autoregressive Process

Music City Center 

Air pollution and associated meteorological conditions, including wind direction, wind speed, temperature, and pressure, are typically collected and reported at regular intervals by monitoring stations. The data produced by these monitoring stations can be incomplete due to technical/mechanical errors, systemic issues (recording only once every 3 hours rather than hourly), or other potential complications. In this paper, we develop a novel imputation method for incomplete angular time series by imposing an autoregressive structure on the projected normal distribution. The imputations can then used in a multiple imputation scheme to create several completed data sets and several corresponding fitted models with Rubin's rules or MCMC posterior stacking to combine the estimates. The proposed method was validated using simulation studies based on autoregressive regression models for a simulated PM2.5 response with wind direction and speed as predictors. We used our proposed imputation methods to model daily PM2.5 data, wind direction, and wind speed collected from the EPA's Air Quality System.

missing data

wind

directional data

multiple imputation

Bayesian statistics 

Section on Bayesian Statistical Science