In this paper, we study the effects of the variations of the propagation delay over large-scale antenna-arrays used in massive multiple-input multiple-output (MIMO) wideband communication systems on the statistical properties of the channel. Due to its simplicity and popularity, the Elliptical geometry-based stochastic channel model (GBSM) is employed to demonstrate new non-stationary properties of the channel in the frequency and spatial domains caused by the drift of delays. In addition, we show that the time of travel of multi-path components (MPCs) over large-scale arrays may result in overlooked frequency and spatial decorrelation effects. These are theoretically demonstrated by deriving the space-time-frequency correlation functions (STFCFs) of both narrowband and wideband Elliptical models. Closed-form expressions of the array-variant frequency correlation function (FCF), power delay profile (PDP), mean delay, and delay spread of single- and multi-confocal Elliptical models are derived when the angles of arrival (AOAs) are von Mises distributed. In such conditions, we find that the large dimensions of the antenna array may limit the narrowband characteristic of the single-ellipse model and alter the wideband characteristics (PDP and FCF) of the multi-confocal Elliptical channel model. Although we present and analyze numerical and simulation results for a particular GBSM, similar conclusions can be extended to other GBSMs.