Effect of Quantisation of a Signal on the Estimated Spectrum
I don't think the quantization is your problem, but how was the data collected?  Have you condidered the possibility of some higher frequency noise aliasing down to 0.25 Hz?  I had that problem once at a much higher frequency, where a funny spike worked its way in to the data, and it turned out to be aliased from a much higher frequency, despite 8-pole Butterworths on every input to the DAC.  Are you anti-alias filtering?