Top plots: GLS spectra of RA (left) and Dec (right) of VLBI astrometry measurements of the source J0204+1415 over nearly 30 years. The vertical blue lines indicate the peak (maximum) period value of 7.9 years in both co-ordinates. The horizontal red line marks the level below which the FAP (false alarm probability) is higher than 5% (VanderPlas 2018). Bottom plots: Temporal variations of RA (left) and Dec (right) of VLBI astrometric measurements centred to the J2000.0 position RA = 02^h04^min50.4138^s and Dec = +15°  14′ 11.043″ (Xu et al. 2019). The trend with coefficients from Table 1 has been removed. The observational data points are shown in black with their formal ±1σ error bars. An apparent decrease in data time density after ∼2009 is due to the recognised anomalous astrometric behaviour and exclusion of the source from regular IVS observing runs (see Section 2 for explanation and reference). The blue curves represent the model fit with parameters listed in Table 1. The shaded blue area around the blue curves indicates the 99.73% confidence interval (±3σ) for the model prediction.