Discharge current and local plasma oscillations are studied in a high voltage Hall effect thruster PPS®-XOOO. Characteristic time scales that appear in different operating conditions are resolved with the use of Hilbert-Huang spectra (HHS) which display time dependenc of instantaneous frequency and power. Sets of intrinsic mode functions (i'm/s) that are used for HHS calculation result due to application of empirical mode decomposition method (EMD) to nonstationary multicomponent signals. In the experiment the signals are captured in the electric circuit of the thruster as well locally, in the vicinity of the thruster exhaust region. Classical electric probes spaced along the azimuth and/or thruster axis let us study correlations of signals which were captured in different locations. In this way azimuthal and axial propagation of disturbances is inspected. The discharge voltage is varied in the range of 200 -^ 900 V while xenon mas flow rate of 5 -^ 9 mg/s. LF, MF, and HF characteristic bands that are known from previous studies of PPS®-100 thruster have been also detected here. However, expanding discharge current onto a set of intrinsic modes we can resolve MF mode more reliably than before. Moreover, for higher discharge voltages, this irregular mode turns into more regular waveform and tends to dominate in the discharge current masking almost completely the breathing mode (LF oscillations of the discharge current). In such a case triggering of HF oscillations is correlated with the phase of MF mode while in the case of PPS®-100 thruster it was correlated with the appropriate phase of the breathing mode (LF band). Regular HF emission that can be unambiguously interpreted as azimuthal electrostatic wave now is observed only in the specific operating conditions of the thruster. However, even if irregular HF emission is observed the time delay of cross-correlated signals which are captured in different azimuthal locations corresponds to the velocity of azimuthal electron drift in the field of magnetic barrier.