This Demonstration analyzes a series of values for apparent magnitude (red band) versus time for a Cepheid variable star. The star has a period of 2.21138771 days based on a best fit of the signal. The axis represents time folded at different period lengths and the axis represents relative event counts from a detector.
The Demonstration is an example of how difficult it is to positively identify unevenly timed, short-period variables in noisy data. In such cases you usually see only noise. However, using different possible periods, if you transform the data to a period that is very close to the correct one, you can see the periodic signal. What originally looked like pure noise is actually random-time sampling of a rapidly varying but periodic series with a modest amount of additional remaining noise. Detecting such periods—finding the 2.2113877 day value and noticing that at that value the signal reveals a periodic base—is a classic example of a computationally difficult problem in astronomical time-series analysis.
The MACHO Project is searching for dark matter in the form of Massive Compact Halo Objects (MACHOs) using gravitational microlensing. The search for these events is done by monitoring over 10 million stars every night in the large Magellanic cloud and galactic bulge using the dedicated 50-inch telescope at Mt. Stromlo.
Other astronomers analyze MACHO data looking for various kinds of objects, including the Cepheid variable studied here.