The paper investigates the effects of three types of nonstationarities on detrended fluctuation analysis (DFA), a method used to quantify long-range power-law correlations in signals. The nonstationarities considered are: (1) removing segments from a signal and stitching the remaining parts, (2) adding random spikes to a signal, and (3) generating signals with segments having different properties (e.g., different standard deviations or correlation exponents). The study finds that these nonstationarities can lead to crossovers in the scaling behavior of the signals. Specifically, the cutting procedure affects anti-correlated signals, causing a crossover from anti-correlation to uncorrelation at small scales. For signals with random spikes, the scaling behavior is a superposition of the signal's scaling and the apparent scaling of the spikes. For signals with different local behaviors, the scaling behavior is a superposition of the scaling of the different components. The paper also provides strategies for pre-processing data to minimize the effects of nonstationarities and discusses how to interpret DFA results for complex signals with different local characteristics.The paper investigates the effects of three types of nonstationarities on detrended fluctuation analysis (DFA), a method used to quantify long-range power-law correlations in signals. The nonstationarities considered are: (1) removing segments from a signal and stitching the remaining parts, (2) adding random spikes to a signal, and (3) generating signals with segments having different properties (e.g., different standard deviations or correlation exponents). The study finds that these nonstationarities can lead to crossovers in the scaling behavior of the signals. Specifically, the cutting procedure affects anti-correlated signals, causing a crossover from anti-correlation to uncorrelation at small scales. For signals with random spikes, the scaling behavior is a superposition of the signal's scaling and the apparent scaling of the spikes. For signals with different local behaviors, the scaling behavior is a superposition of the scaling of the different components. The paper also provides strategies for pre-processing data to minimize the effects of nonstationarities and discusses how to interpret DFA results for complex signals with different local characteristics.