Raman spectra of rutile titanium dioxide (TiO_2) were measured at temperatures from 100 to 1150 K. Each Raman mode showed unique changes with temperature. Beyond the volume-dependent quasiharmonicity, the explicit anharmonicity was large. A new method was developed to fit the thermal broadenings and shifts of Raman peaks with a full calculation of the kinematics of three-phonon and four-phonon processes, allowing the cubic and quartic components of the anharmonicity to be identified for each Raman mode. A dominant role of phonon-phonon kinematics on phonon shifts and broadenings is reported. Force-field molecular dynamics calculations with the Fourier-transformed velocity autocorrelation method were also used to perform a quantitative study of anharmonic effects, successfully accounting for the anomalous phonon anharmonicity of the B_1_(g) mode
