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

Dispersion measure variability for 36 millisecond pulsars at 150MHz with LOFAR