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I have read that in speech signal processing analysis when voice is segmented in brief temporary segments the series segments transitions from being non stationary to stationary. My question is if this is also the case for financial data when this data can be segmented in smaller and smaller time spand windows (stock market).

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Financial market trading data is thought to be fractal in dimension and thus not sufficiently band-limited before sampling. So smaller windows might not have any effect on improving pseudo-stationarity.

Whereas the physical processes behind speech production are better understood and more physically limited (the rate of human muscle contractions controlling lung, larynx, and head cavity resonances, etc.), as well as the sound capture being low-pass filtered below typical human hearing thresholds before sampling above the Nyquist rate.

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