Variations in scaling behavior in the flux and emissions of distant astronomical sources with respect to their cosmic time are important phenomena that can provide valuable information about the dynamics within the sources and their cosmological evolution with time. Different studies have been applying linear analysis to understand and model quasars' light curves. Here, we study the multifractal behavior of selected quasars' radio emissions in their observed frame (at 22 and 37 GHz bands) and their rest frame. To this end, we apply the wavelet transform-based multifractal analysis formalism called wavelet transform modulus maxima. In addition, we verify whether the autoregressive integrated moving average (ARIMA) models fit our data. In our work, we observe strong multifractal behavior for all the sources. Additionally, we find that the degree of multifractality is strongly similar for each source and significantly different between sources at 22 and 37 GHz. This similarity implies that the two frequencies have the same radiation region and mechanism, whereas the difference indicates that the sources have intrinsically different dynamics. Furthermore, we show that the degree of multifractality is the same in the observed and rest frames of the quasars, i.e., multifractality is an intrinsic property of radio quasars. Finally, we show that the ARIMA models fit the 3C 345 quasar at 22 GHz and partially fit most of the time series, with the exception of the 3C 273 and 3C 279 quasars at 37 GHz, for which the models are found to be inadequate.