To study the nonlinear characteristics of changes in the Earth's rotation rate, a comprehensive analysis of the nonlinear characteristics of the length of day (ΔLOD) observations reflecting changes in the Earth’s rotation rate is conducted from multiple perspectives, including periodicity, chaos, and fractal, by using the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), recursive quantitative analysis (RAQ), and Grassberger-Procaccia (GP) algorithms. The long-term high-accuracy ΔLOD observations from January 1, 1962 to December 31, 2023, were comprehensively and reliably analyzed and then used as dataset published by the International Earth Rotation and Reference Systems Service, IERS) 14C04 series. The present workfocuses on comparing and analyzing whether there are any significant differences in the ΔLOD characteristics before and after deducting the periodic or chaotic components of ΔLOD time series. The main conclusions obtained are as follows. 1) The ΔLOD time series consists of the well-known trend components, many periodic components, and chaotic components, and therefore can be characterized by obvious multi timescales, chaotic dynamics, and fractal structure. The characteristics were not considered in previous research. 2) The period of the ΔLOD time series after deducting the chaotic components is exactly the same as the period of the original ΔLOD time series, implying that the chaotic components have no effects on reconstruction nor analysis of the periodic components. 3) There is no significant difference in chaotic characteristics between the original ΔLOD time series and its time series after deducting trend and periodic components, but the complexity of the fractal structure of the former is relatively stronger. Not only can this work provide a valuable reference for studying the mechanism of changes in the Earth’s rotation rate, but also model such rotation changes and then predict the chances on different timescales.