Adjusted functional boxplots for spatio-temporal data visualization and outlier detection

This article proposes a simulation-based method to adjust functional boxplots for correlations when visualizing functional and spatio-temporal data, as well as detecting outliers. We start by investigating the relationship between the spatio-temporal dependence and the 1.5 times the 50% central region empirical outlier detection rule. Then, we propose to simulate observations without outliers on the basis of a robust estimator of the covariance function of the data. We select the constant factor in the functional boxplot to control the probability of correctly detecting no outliers. Finally, we apply the selected factor to the functional boxplot of the original data. As applications, the factor selection procedure and the adjusted functional boxplots are demonstrated on sea surface temperatures, spatio-temporal precipitation and general circulation model (GCM) data. The outlier detection performance is also compared before and after the factor adjustment.