Testing ETH Price-Run Lengths Against an Independent-Periods Null
Summary
The document examines a reported average duration of roughly 25 minutes for continuous ETH price rises or falls, measured in five-minute intervals over three months. The response recommends defining what would count as unusual and comparing the observation with a null model. Under independent periods with a fixed probability of an upward move, it derives the expected run length for declines; when the probability is one half, the expectation is two periods.
The analysis also warns that excluding price changes below $20 can bias measured runs toward longer durations, because smaller moves are more likely to occur over short intervals. The size of that effect depends on time-specific volatility. A further response raises liquidity, trading volume, and market efficiency as factors to investigate. The document supplies a simple benchmark and caveats, but no underlying price data, statistical test, or conclusion about whether ETH’s observed runs are unusual.
Key ideas
- Compare observed price-run lengths with a clearly specified null model before calling them unusual.
- With independent periods and a 50% chance of an upward move, the expected declining run is two periods.
- Filtering out small price changes can remove short runs and raise measured run duration.
- The impact of a price threshold depends on volatility at the sampling horizon.
- Liquidity and trading volume may affect the interpretation of observed ETH price movements.
Tags
Full text
# Ethereum Price Movements
# Ethereum Price Movements
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.
## Answer by Matthew Gunn (score 2, accepted)
https://quant.stackexchange.com/a/37553
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.
## Answer by user31219 (score -1)
https://quant.stackexchange.com/a/37554
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.