I am specifically working on a categorical time series of best n number of parallel threads (for n=1..16) for a multicore workstation. I constructed the Walsh-Fourier periodogram for size 2^10 and 2^11 data points. Both of the images are with the first value removed to allow a scaled image. The difference is dramatic as you can see.
My naive interpretation is that there is something stationary going on with the $2^{11}$ range that isn't happening in the $2^{10}$ range. In particular my data covers minute intervals and if I am looking for background programs that will effect the the best thread policy, if they are scheduled nightly (antivirus, back-up etc) then in terms of 1440 minutes=1 day they will fall within $2^{11}$ minutes because $2^{10}<1440<2^{11}$. Am I making the correct assumption here?
Because I am too new on this particular stackexchange I am not allowed to post the periodograms but they are hosted here.