Fractal analysis is applied in a variety of research fields to characterize nonstationary data. Here, fractal analysis is used as a tool of characterization in time series. The fractal dimension is calculated by Higuchi’s method, and the effect of small data size on accuracy is studied in detail. Three types of fractal-based anomaly indicators are adopted: (a) the fractal dimension, (b) the error of the fractal dimension, and (c) the chisquare value of the linear fitting of the fractal curve in the wave number domain. Fractal features of time series can be characterized by introducing these three measures. The proposed method is applied to various simulated fractal time series with ramp, random, and periodic noise anomalies and also to neutron detector signals acquired in a nuclear reactor. Fractal characterization can successfully supplement conventional signal analysis methods especially if nonstationary and non-Gaussian features of the signal become important.