  Efforts are underway to use high-precision timing of pulsars in order to
detect low-frequency gravitational waves. A limit to this technique is the
timing noise generated by dispersion in the plasma along the line of sight to
the pulsar, including the solar wind. The effects due to the solar wind vary
with time, influenced by the change in solar activity on different time scales,
ranging up to $\sim 11$ years for a solar cycle. The solar wind contribution
depends strongly on the angle between the pulsar line of sight and the solar
disk, and is a dominant effect at small separations. Although solar wind models
to mitigate these effects do exist, they do not account for all the effects of
the solar wind and its temporal changes. Since low-frequency pulsar
observations are most sensitive to these dispersive delays, they are most
suited to test the efficacy of these models and identify alternative
approaches. Here, we investigate the efficacy of some solar wind models
commonly used in pulsar timing using long-term, high-cadence data on 6 pulsars
taken with the Long Wavelength Array, and compare them with an operational
solar wind model. Our results show that stationary models of the solar wind
correction are insufficient to achieve the timing noise desired by pulsar
timing experiments, and we need to use non-stationary models, which are
informed by other solar wind observations, to obtain accurate timing residuals.
