Lloyd said:
I guess the same question applies to the Cepheids. Does the data on them show some variation in the time between changes in brightness?

Cepheids vary on a period of days to weeks, and some theorists (e.g., myself) believe that even longer periods, such as the 11-year cycle of our Sun, are caused by the same mechanism. I "think" that the period is relatively precise, and the changes in luminosity are sine waves, at least to the limits of the instrumentation. I'll try to locate some data on this.