On a more serious note, I am a beginner at this corner of analysis, but it took maybe thirty minutes to determine that leap year is a problem and a few days to determine that it is, more properly, a major pain in the rump (I am working with linear regressions day-wise, and they fall apart if the days do not match up).
Restating dates as fractional years is not bad, but pinning them to December 31st is. For my work, I've used whole number days, but pinned them to the date and time of the winter solstice. This leaves a dislocation when the equinox jumps between, say 1002 hours to 1359 hours (the former rounding to the previous day and the latter to the next) and it also leaves a leap day equivalent the day before the solstice. In practical terms, little is happening that time of the year ice-wise, and locking most of the year to the solar calendar improves the quality of regressions through the period of active analysis (at the cost of what ends up being 3-14 days of disturbed numbers in late December).
Below is a chart of the behavior of the summer solstice (shamelessly lifted from Wikipedia). By restating my data, I still have the underlying four year cycle, but have taken out the long term drift. As an aside, we have the Gregorian Calendar to thank for the fact there was no hundred year reset, which from today's perspective would have neatly divided the satellite record into nearly even halves.
I could use a precise annual fractional date (avoiding the rounding skip when the solstice jumps between morning and afternoon) but convinced myself there would be no point - this would add only false precision. The daily figures (from whatever source) are not based on a daily snapshot at 0000 or 1200 hours UT, but are rather based on whatever and whenever the satellite(s) served up throughout that day, based on their orbital mechanics and other conditions. To be anything like rigorous, you'd have to also regroup the orbit by orbit data streams to solar days rather than calendar days (and please, don't even talk about sidereal days - we - I'm pretty sure - don't care about them in this context, despite their role in orbital mechanics).
The real lesson to all of this is exactly as JimD stated above - if you are hanging on day to day numbers, be it daily changes or year to year comparisons, what is catching your eye is almost certainly more noise than signal. A good example is "do the peaks occur later (or earlier) now" - they may or may not, but unless all the underlying analysis effectively addresses the difference between the solar and calendar years, it is likely to misstate the picture, because any actual change is on a comparable scale to the equinox progression over the years of satellite record.
