Imputation of missing values in environmental time series by D-vine copulas

Abstract

Missing values in environmental time series are common and must be imputed before carrying out an analysis requiring complete data. We propose an imputation method for the time series of a target station using information of neighboring stations measuring the same variable. The method allows these neighboring stations to have missing values themselves. The multivariate dataset comprising the time series of the target station and its neighboring stations is jointly modeled by a vine copula and parametric margins. Multiple imputation takes into account the uncertainty of missing data by generating several plausible values for each missing value in the time series of the target station. This is done in a Bayesian framework by sampling the posterior distribution of a missing value, which is conditional on the observed stations for the date. The method is suitable for extremes because the vine copula can model the eventual tail dependence between stations. The application to a skew surge time series is presented, with cross-validated results and a focus on the performance for the upper extremes.

Keywords

• Missing value
• Multiple imputation
• Extreme value
• Vine copula
• Bayesian inference