Installing Phasor Measurement Units (PMUs) in the smart grid has played an important role in having more reliable and secure grid. Due to the high sampling rate (50 samples/s), PMU generates massive amount of data compared to the conventional SCADA system. Understanding the mathematical and statistical characteristics of the PMU data is a very crucial step to perform accurate modeling and estimation of the power system variables (Voltage (V), frequency (f), and phase angle (θ)). In this paper, we show the non-stationarity of the PMU data by applying Augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests on a large data set from the EPFL campus grid. Then, we study the fractality of the PMU data by estimating the differencing parameter (d) in the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model. Our results call for adoption of ARFIMA models to model the PMU data in the smart grid.