  Radio pulses from pulsars are affected by plasma dispersion, which results in
a frequency-dependent propagation delay. Variations in the magnitude of this
effect lead to an additional source of red noise in pulsar timing experiments,
including pulsar timing arrays that aim to detect nanohertz gravitational
waves.
  We aim to quantify the time-variable dispersion with much improved precision
and characterise the spectrum of these variations.
  We use the pulsar timing technique to obtain highly precise dispersion
measure (DM) time series. Our dataset consists of observations of 36
millisecond pulsars, which were observed for up to 7.1 years with the LOFAR
telescope at a centre frequency of ~150 MHz. Seventeen of these sources were
observed with a weekly cadence, while the rest were observed at monthly
cadence.
  We achieve a median DM precision of the order of 10^-5 cm^-3 pc for a
significant fraction of our sources. We detect significant variations of the DM
in all pulsars with a median DM uncertainty of less than 2x10^-4 cm^-3 pc. The
noise contribution to pulsar timing experiments at higher frequencies is
calculated to be at a level of 0.1-10 us at 1.4 GHz over a timespan of a few
years, which is in many cases larger than the typical timing precision of 1 us
or better that PTAs aim for. We found no evidence for a dependence of DM on
radio frequency for any of the sources in our sample.
  The DM time series we obtained using LOFAR could in principle be used to
correct higher-frequency data for the variations of the dispersive delay.
However, there is currently the practical restriction that pulsars tend to
provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM
precision at low frequencies, but not both, due to spectral properties.
Combining the higher-frequency ToAs with those from LOFAR to measure the
infinite-frequency ToA and DM would improve the result.
