The increased operational stresses and the aging effect have increased the instances of device malfunctions and failures in the grid. The malfunction/ failure of critical devices such as instrument transformers, breakers, etc cause unwanted supply disruptions and composite system outages. These device-level malfunctions produce unique dynamic signatures, which can be detected/segregated at phasor measurement units (PMUs) using localized data analytics with low processing delays. This work focuses on the detection and identification of ferroresonance (FR) type failures in capacitive voltage transformers (CVTs) in high-voltage transmission systems at the PMU level. For this, firstly the effect of CVT-FR on phasor measurements through frequency response characterization and sensitivity analysis is observed. Thereafter, a divergent density estimation supported intrinsic mode function method is proposed to distinguish FR events from system-level disturbances like faults, generation loss, etc., in the phasor measurements. The divergent density estimation captures the statistical distribution of intrinsic mode functions (IMFs) under perturbation and acquires unique mode signatures corresponding to FR. IMFs are obtained by applying empirical mode decomposition on the raw phasor trends. The proposed method is tested with simulated cases for different CVT models in Matlab/Simulink and real system data in the Eastern region of the India grid.