Real time stationarity test

External question — Quantitative Finance Stack Exchange Author: Krzysztof Fajst Original post: https://quant.stackexchange.com/questions/25876 License: CC BY-SA 3.0 — https://creativecommons.org/licenses/by-sa/3.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I have a trading system based on Machine Learning which is trading 8 symbols intraday. From the results I found out that some weeks of trading are successful for some symbols, then it usually switches to unsuccessful next week for previously successful symbol. At the same time another symbol which was unsuccessful previous week start to be successful this week. As an explanation to this phenomenon it comes to my mind that the underlying symbol series switching from stationary to non stationary and vice versa. So my question is: did somebody tried intraday (1 min data) stationarity test on FOREX or S&P ??? I believe such test should be'data window based' with sliding window than what would be a size of such window ??? What method would be the best for such test (DF, ADF, KPSS ) or other ??? regards, Krzysztof

External answer — Quantitative Finance Stack Exchange Author: dkhokhlov Original post: https://quant.stackexchange.com/a/26000 License: CC BY-SA 3.0 — https://creativecommons.org/licenses/by-sa/3.0/ Adaptation: HTML converted to plain text; contact email addresses removed. We assume weak stationarity definition. Price level is non-stationary. Trend-stationarity is like following a trend, not working on this time scale. So need to use returns. Returns on interval <15min are dominated by bid-ask bounce. Useless, trap. So test should be using >15min returns on window interval W < (hold time / N), N = 2-4. Then Unit root test p value can give some degree of stationarity to speculate further in context of specific trading system.