A motion trajectory prediction (MTP) - based brain-computer interface (BCI) aims to reconstruct the three-dimensional (3D) trajectory of upper limb movement using electroencephalography (EEG). The most common MTP BCI employs a time series of bandpass-filtered EEG potentials (referred to here as the potential time-series, PTS, model) for reconstructing the trajectory of a 3D limb movement using multiple linear regression. These studies report the best accuracy when a 0.5-2Hz bandpass filter is applied to the EEG. In the present study, we show that spatiotemporal power distribution of theta (4-8Hz), mu (8-12Hz), and beta (12-28Hz) bands are more robust for movement trajectory decoding when the standard PTS approach is replaced with time-varying bandpower values of a specified EEG band, ie, with a bandpower time-series (BTS) model. A comprehensive analysis comprising of three subjects performing pointing movements with the dominant right arm toward six targets is presented. Our results show that the BTS model produces significantly higher MTP accuracy (R~0.45) compared to the standard PTS model (R~0.2). In the case of the BTS model, the highest accuracy was achieved across the three subjects typically in the mu (8-12Hz) and low-beta (12-18Hz) bands. Additionally, we highlight a limitation of the commonly used PTS model and illustrate how this model may be suboptimal for decoding motion trajectory relevant information. Although our results, showing that the mu and beta bands are prominent for MTP, are not in line with other MTP studies, they are consistent with the extensive literature on classical multiclass sensorimotor rhythm-based BCI studies (classification of limbs as opposed to motion trajectory prediction), which report the best accuracy of imagined limb movement classification using power values of mu and beta frequency bands. The methods proposed here provide a positive step toward noninvasive decoding of imagined 3D hand movements for movement-free BCIs.