We study the evolution of the temporal properties of MAXI J1820+070 during the 2018 outburst in its hard state from MJD 58,190 to 58,289 with Insight-HXMT in a broad energy band 1-150 keV. We find different behaviors of the hardness ratio, the fractional rms and time lag before and after MJD 58,257, suggesting a transition occurred around this point. The observed time lags between the soft photons in the 1-5 keV band and the hard photons in higher energy bands, up to 150 keV, are frequency-dependent: the time lags in the low-frequency range, 2-10 mHz, are both soft and hard lags with a timescale of dozens of seconds but without a clear trend along the outburst; the time lags in the high-frequency range, 1-10 Hz, are only hard lags with a timescale of tens of milliseconds; they first increase until around MJD 58,257 and decrease after this date. The high-frequency time lags are significantly correlated to the photon index derived from the fit to the quasi-simultaneous NICER spectrum in the 1-10 keV band. This result is qualitatively consistent with a model in which the high-frequency time lags are produced by Comptonization in a jet.