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I've noticed a strange pattern for ethereum (ETH) prices over the past 3 months such that when sampling with a resolution of five minutes the mean time a continuous price drop/increase took ~25 minutes with a median of ~23 minutes. I factored out price shifts smaller than $20 from consideration.

Does this make sense? I have the distinct feeling that there's some first principles mistake I'm missing here.

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  • $\begingroup$ If you don't exclude price shifts smaller than $20, do you get approximately 10 minutes? $\endgroup$ – Matthew Gunn Jan 2 '18 at 0:27
  • $\begingroup$ why not filtering on % instead of $20? $\endgroup$ – mbison Jan 2 '18 at 11:28
  • $\begingroup$ Without any exclusion the mean drops to ~16 minutes with a median of ~15 minutes $\endgroup$ – Tsahi Halyo Jan 3 '18 at 5:18
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To say something is "strange," shouldn't you have some clean, careful analysis of what is expected? what you wouldn't consider strange?

Null hypothesis of independent time periods with $\rho$ chance of going up:

If each period is independent and has a $\rho \in (0, 1)$ chance of going up, there is:

  • $\rho$ chance of a 1 period price decline
  • $(1 - \rho)\rho$ chance of a 2 period price decline
  • $(1 - \rho)^2 \rho$ chance of a 3 period price decline etc...

The expected number of consecutive periods with declining prices can be computed using series as:

\begin{align*} \lim_{n \rightarrow \infty} \rho \sum_{i=0}^n ( i + 1) (1 - \rho)^i &= \rho \left( \frac{1}{\rho} + \frac{1 - \rho}{\rho^2}\right)\\ &= 1 + \frac{1 - \rho}{\rho} \end{align*}

So if $\rho = .5$, the expected number of consecutive, declining periods is 2 periods (or 10 minutes in the case of 5 minute periods).

If you exclude price changes less than $20 (approx. 3%), you're more likely to exclude price changes that occur over fewer periods! How big of an effect this is depends on the time specific price volatility, but since 3% is quite big compared to 5 minute volatility, your exclusion rule is going to change things quite a bit.

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What are your criteria for believing the ETH is efficient? Have you ruled out thin markets due to lack of demand, lack of supply, or lack of liquidity for trades? What is the volume at different times you attempt to trade or sample prices? Is the volume concentrated in a few trades or is it the result of motivated sellers meeting motivated buyers? Just as an obvious point, TBills are a pretty efficient market, Da Vinci paintings are not. I guess ETH is closer to Salvador Mundi than to the 90 day bill.

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