Are time series data always contain noise?
Periodically taken ticker data is very likely not a set of samples of a band-limited function, thus can contain aliasing artifacts which can be considered noise.  This is possibly a much larger contribution than quantization and time jitter noise.

Absence of noise requires the existence of well defined signal being measured.  Proving that such a signal really exists is a separate and likely far more difficult problem for some types of time series.