We have performed nuclear quadrupole resonance (NQR) experiments on $^{47}$Ti nuclei in Dy$_2$Ti$_2$O$_7$ in the temperature range 70 -- 300 K in order to investigate the dynamics of $4f$ electrons with strong Ising anisotropy. A significant change o
f the NQR frequency with temperature was attributed to the variation of the quadrupole moment of Dy $4f$ electrons. A quantitative account was given by the mean field analysis of the quadrupole-quadrupole (Q-Q) interaction in the presence of the crystalline-electric-field splitting. The magnitude and the temperature dependence of the nuclear spin-lattice relaxation rate was analyzed, including both the spin-spin and the Q-Q interactions. The results indicate that these two types of interaction contribute almost equally to the fluctuation of Dy magnetic moments.
