  Data depth is an efficient tool for robustly summarizing the distribution of
functional data and detecting potential magnitude and shape outliers. Commonly
used functional data depth notions, such as the modified band depth and
extremal depth, are estimated from pointwise depth for each observed functional
observation. However, these techniques require calculating one single depth
value for each functional observation, which may not be sufficient to
characterize the distribution of the functional data and detect potential
outliers. This paper presents an innovative approach to make the best use of
pointwise depth. We propose using the pointwise depth distribution for
magnitude outlier visualization and the correlation between pairwise depth for
shape outlier detection. Furthermore, a bootstrap-based testing procedure has
been introduced for the correlation to test whether there is any shape outlier.
The proposed univariate methods are then extended to bivariate functional data.
The performance of the proposed methods is examined and compared to
conventional outlier detection techniques by intensive simulation studies. In
addition, the developed methods are applied to simulated solar energy datasets
from a photovoltaic system. Results revealed that the proposed method offers
superior detection performance over conventional techniques. These findings
will benefit engineers and practitioners in monitoring photovoltaic systems by
detecting unnoticed anomalies and outliers.
