This paper draws parallels between the Principal Components Analysis of factorless high-dimensional nonstationary data and the classical spurious regression. We show that a few of the princpal components of such data absorbs nearly all the data variation. The corresponding scree plot suggests that the data contains a few factors, which is collaborated by the standard panel information criteria. Furthermore, the Dickey-Fuller tests of the unit root hypothesis applied to the estimated 'idiosyncratic terms' often reject, creating an impression that a few factors are responsible for most of the nonstationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences.