This paper investigates the effects of trends—linear, periodic, and power-law—on the scaling behavior of detrended fluctuation analysis (DFA) applied to noisy signals. DFA is a method used to estimate long-range power-law correlation exponents in signals. However, trends in real-world data can distort DFA results, making it challenging to interpret the true correlation properties of the signal. The study systematically examines how different types of trends affect the scaling results of DFA and identifies the conditions under which crossovers in the scaling behavior occur. The research shows that crossovers in the scaling behavior of signals with trends arise from the competition between the scaling of the noise and the "apparent" scaling of the trend. The study finds that the position of these crossovers follows a long-range power-law dependence on the parameters of the trends. The paper also demonstrates that the DFA result for a signal with a trend can be determined by the superposition of the DFA results for the noise and the trend, assuming they are independent. If this superposition rule is not followed, it indicates that the noise and trend are not independent, and removing the trend could alter the correlation properties of the noise. The study provides examples of real-world data where these trends are likely to occur, such as particle emissions, air density, temperature, and earthquake occurrences. It also discusses how to use DFA appropriately to minimize the effects of trends and how to distinguish between crossovers caused by trends and those indicating a transition in the underlying correlation properties of the data. The paper analyzes the scaling behavior of signals with linear, periodic, and power-law trends, showing how the crossover scales depend on the parameters of the trends and the correlation properties of the noise. It also demonstrates that the scaling behavior of signals with trends can be understood through the superposition rule, which allows for the determination of whether trends are independent of the noise. The study concludes that DFA is a reliable method for quantifying correlations in noisy signals embedded in polynomial trends, and that the scaling and crossover features of DFA can be used to identify the presence and order of polynomial trends in the data.This paper investigates the effects of trends—linear, periodic, and power-law—on the scaling behavior of detrended fluctuation analysis (DFA) applied to noisy signals. DFA is a method used to estimate long-range power-law correlation exponents in signals. However, trends in real-world data can distort DFA results, making it challenging to interpret the true correlation properties of the signal. The study systematically examines how different types of trends affect the scaling results of DFA and identifies the conditions under which crossovers in the scaling behavior occur. The research shows that crossovers in the scaling behavior of signals with trends arise from the competition between the scaling of the noise and the "apparent" scaling of the trend. The study finds that the position of these crossovers follows a long-range power-law dependence on the parameters of the trends. The paper also demonstrates that the DFA result for a signal with a trend can be determined by the superposition of the DFA results for the noise and the trend, assuming they are independent. If this superposition rule is not followed, it indicates that the noise and trend are not independent, and removing the trend could alter the correlation properties of the noise. The study provides examples of real-world data where these trends are likely to occur, such as particle emissions, air density, temperature, and earthquake occurrences. It also discusses how to use DFA appropriately to minimize the effects of trends and how to distinguish between crossovers caused by trends and those indicating a transition in the underlying correlation properties of the data. The paper analyzes the scaling behavior of signals with linear, periodic, and power-law trends, showing how the crossover scales depend on the parameters of the trends and the correlation properties of the noise. It also demonstrates that the scaling behavior of signals with trends can be understood through the superposition rule, which allows for the determination of whether trends are independent of the noise. The study concludes that DFA is a reliable method for quantifying correlations in noisy signals embedded in polynomial trends, and that the scaling and crossover features of DFA can be used to identify the presence and order of polynomial trends in the data.