  Owing to technological advances, the number of exoplanets discovered has
risen dramatically in the last few years. However, when trying to observe Earth
analogs, it is often difficult to test the veracity of detection. We have
developed a new approach to the analysis of exoplanetary spectral observations
based on temporal multifractality, which identifies time scales that
characterize planetary orbital motion around the host star, and those that
arise from stellar features such as spots. Without fitting stellar models to
spectral data, we show how the planetary signal can be robustly detected from
noisy data using noise amplitude as a source of information. For observation of
transiting planets, combining this method with simple geometry allows us to
relate the time scales obtained to primary and secondary eclipse of the
exoplanets. Making use of data obtained with ground-based and space-based
observations we have tested our approach on HD 189733b. Moreover, we have
investigated the use of this technique in measuring planetary orbital motion
via Doppler shift detection. Finally, we have analyzed synthetic spectra
obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the
influence of the presence of a planet or a spot on that spectrum over one
orbital period. We have demonstrated that, so long as the signal-to-noise-ratio
$\ge$ 75, our approach reconstructs the planetary orbital period, as well as
the rotation period of a spot on the stellar surface.
