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tokens: and 3C 273 we get signs of local nonstationarity that are not consistent among the various tests, for Mrk 421 we get multiple clues that may indicate local nonstationarity synchronous with large changes in its average flux. While we do not find any significant change in the PSD between multiple epochs for the same blazar we must note that a small temporal change in the PSD of red-noise variability may not always be detectable with the quality of data that is available. There may be an excess scatter in the binned PSD estimates obtained from light curves spanning hours to years leading to poor fits of a model PSD and subsequently higher rejection probabilities. Sampling window and Poisson noise give rise to distortions in the PSD, which are difficult to quantify, and cause uncertainties in the estimates of PSD slopes, which can eclipse any change in the slope of the PSD of the underlying process. In alternative methods of PSD modeling, such as CARMA, the difficulties in discerning a local nonstationary process persist. Kelly et al. ( 2014 ) showed, using an irregularly sampled simulated light curve stitched together from two separate stationary CARMA processes with differing variances, that a CARMA (5,2) model provided a good fit, as if the complete light curve was a single stationary process. It is as if the PSD of the combined process is a blend of the separate processes weighted according to their respective S/Ns. The local nonstationarity in the PSD of the X-ray variability of Seyfert galaxies such as IRAS 13224−3809 has been explained as being due to having an accretion rate close to the Eddington limit, or deformations in a time-evolving corona (Wilkins Gallo 2015 ; Alston et al. 2020 ). In the blazars the X-ray emission is mostly from the jet, thus if it exhibits local nonstationarity that will imply some important change in the emission process inside the jet. Alternatively, the jet variability may be driven by fluctuations in the accretion disk and in that case the nonstationarity may be due to specific kinds of changes in the disk. We find a linear flux–rms relation in the X-ray light curves of Mrk 421 separated by a period as long as two decades and over timescales of days to months. It is one of the few cases in which a flux–rms relation has been detected in a blazar across such long timescales. This, along with similar demonstrations in other blazars and other wave bands (Edelson et al. 2013 ; Kushwaha et al. 2017 ), implies that the flux–rms relation may be a ubiquitous feature of blazar variability, similar to other accreting black hole systems, e.g., BHXRBs. There is a significant difference in the best-fit slope of the flux–rms relation among the short-term and long-term observations of Mrk 421 across two decades. This may be the result of some systematic effect like error subtraction or it may be due to local nonstationarity in the source itself. For BHXRBs the slope and the flux intercept are known to depend on the