Let's imagine if you were the god of the markets and you could do whatever you wanted, what would you make of EUR/USD? Which characteristics would you give your timeseries?
My ideal timeseries would be:
- a lot less noise than what is currently present (thank god for digital signal processing)
- a normal probability distribution function (I hate those heavy tails)
- a Hurst exponent of 0.9: very persistent trends
- at least one positive Lyapunov exponent
- all timeseries would be stationary (ADF & PP)
- long Lyapunov time
- low dimensionality & easily embeddable
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Once the Fractal Dimension reaches that level and all other criteria are met, what ensures stationarity non-reversal? Maybe a derivative of the Hurst like its slope?
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