The unstable plastic flow of an AlMg alloy, associated with the Portevin-Le Chatelier effect, was studied near the lower strain-rate boundary of instability using multifractal analysis. Self-similarity of deformation curves, indicating long-range time correlations of stress serrations, was detected within the strain-rate range where serrations are commonly ascribed to the occurrence of uncorrelated deformation bands. The deformation curves display a wide range of shapes that are characterized by different groupings of serrations. Multifractal analysis provides a method to quantify the observed complexity and compare it to known Portevin-Le Chatelier effect regimes. The measurement noise effect on the multifractal spectra determined from experimental data was mimicked by superposing multifractal Cantor sets with random noise. Such tests using standard multifractal data sets justify the separation of self-similar and random components of the serrated deformation curves. Furthermore, these results shed light on the general problem of the effect of experimental noise on the apparent multifractal properties of physical fractals.