  Millisecond pulsars (MSPs) are known for their long-term stability. Using six
years of observations from the Neutron Star Interior Composition Explorer
(NICER), we have conducted an in-depth analysis of the X-ray timing results for
six MSPs: PSRs B1937+21, B1821$-$24, J0437$-$4715, J0030+0451, J0218+4232, and
J2124$-$3358. The timing stability parameter $\sigma_z$ has been calculated,
revealing remarkable timing precision on the order of $10^{-14}$ for PSRs
B1937+21 and J0437$-$4715, and $10^{-13}$ for PSRs B1821$-$24, J0218+4232, and
J0030+0451 over a timescale of 1000 days. These findings underscore the
feasibility of autonomous in-orbit timekeeping using X-ray observations of
MSPs. In addition, the consistency of long-term spin-down noise in the X-ray
and radio bands has been investigated by comparison with IPTA radio data.
