Data imputation and nested seasonality time series modelling for permanent data collection stations: methodology and application to Ontario

Analysis and literature review have indicated that transportation agencies often report significant percentage of missing values of traffic volumes collected at permanent data collection stations (PDCS). These missing values can be as high as 60% in some cases. Although invested significantly in legacy systems that rely primarily on inductive loop detectors to collect traffic volumes, transportation agencies are faced with a challenge of relying only on a small set of the traffic data. Despite the fact that transportation agencies are often required to report on various annual traffic statistics such as average annual daily traffic (AADT) and vehicles miles travelled, little research is available on how transportation practitioners handled missing values in their traffic data collection efforts. In this paper, a simple iterative approach is introduced — based on the integration of an imputation algorithm and a time series model — to impute missing PDCS data. The approach is deigned such that the imputation algorithm is implemented first to impute relatively small to medium gaps forming a library of complete datasets; then a time series model is fitted to these stations to form the base for imputing large gaps. The data imputation algorithm is applied on a case study on Ministry of Transportation of Ontario PDCS stations, Canada. The average errors for imputing as high as 90% of missing data — with maximum continuous gaps of 76 h — were approximately 16% with an average median error of 11 veh/h. After all traffic data are imputed, a time series model is estimated to capture the multiple seasonalities and trends in the traffic data across multiple years. The estimated “model” is then used to calculate and produce seasonal variation factors and graphs that are typically required for planning, design, control, operation, and management of traffic and highway facilities. By estimating the model parameters using existing raw data, the model was then tested to assess its accuracy to forecast future years.