  We present the timing analysis of 10 archived \XMM observations with an
exposure of $>40$ ks of Markarian 421. Mrk 421 is the brightest
high-frequency-peaked BL Lac object (HBL) emitting in X-rays produced by
electrons accelerated in the innermost regions of a relativistic jet pointing
toward us. For each observation, we construct averaged X-ray spectra in 0.5--10
keV band, as well as 100 s binned light curves (LCs) in various subbands.
During these observations, the source exhibited various intensity states
differing by close to an order of magnitude in flux, with the fractional
variability amplitude increasing with energy through the X-ray band. Bayesian
power spectral density analysis reveals that the X-ray variability can be
characterized by a colored noise, with an index ranging from $\sim-1.9$ to
$-3.0$. Moreover, both the standard cross-correlation function and
cross-spectral methods indicate that the amount of time lags increases with the
energy difference between two compared LCs. A time-dependent two-zone jet model
is developed to extract physical information from the X-ray emission of Mrk
421. In the model, we assume that the jet emission mostly comprises a
quasi-stationary component and a highly variable one. Our results show that the
two-zone model can simultaneously provide a satisfactory description for both
the X-ray spectra and time lags observed in different epochs, with the model
parameters constrained in a fully acceptable interval. We suggest that shocks
within the jets may be the primary energy dissipation process responsible for
triggering the rapid variability, although magnetic reconnection cannot be
excluded.
