Active galactic nuclei (AGNs) exhibit complex variability across multiple wavelengths, reflecting diverse physical processes near their central engines. This work investigates the temporal variability of four AGNs, Mrk 509, NGC 5548, NGC 4151, and NGC 4593, using MFDMA (multifractal detrended moving average) analysis and Fisher─Shannon information plane applied to their X-ray, ultraviolet, and optical light curves. These methods quantify the scaling behaviour and complexity of the variability, revealing persistent correlations and distinct variability patterns across energy bands. The Fisher─Shannon analysis further characterizes the degree of stochasticity and structural complexity in the emission processes. Our findings support the interpretation that multifractal and information-theoretic measures provide effective diagnostics of the physical mechanisms driving AGN variability. This study demonstrates the utility of advanced time series techniques as effective diagnostics of AGN variability mechanisms.