How Autocorrelation Relates to Repeated Price Moves

Summary

The document asks how a reported 20% autocorrelation in consecutive Deutsche mark price moves could be connected to a claim that sequences repeated more than half the time. It contrasts this interpretation with the familiar statistical view of autocorrelation as association between observations over time, and with the probability of getting consecutive heads from independent coin flips. A respondent points to a proof relating the probability of successive occurrences to autocorrelation, but the proof itself is not included in the document.

The material therefore raises a useful distinction between correlation as a statistic and the frequency of a particular event, while offering little detail for resolving it. It gives no definitions of the price-move events, no derivation, and no assumptions about the underlying distribution or dependence structure. The cited historical claim and linked explanation cannot be assessed from the text alone, so readers should not treat the stated conversion from correlation to frequency as established here.

Key ideas

• Autocorrelation measures dependence between observations at different times.
• The document questions how autocorrelation could imply a frequency of repeated price moves.
• A respondent says a proof can relate successive-event probability to autocorrelation, but does not reproduce it.
• The text does not specify the event definition or assumptions needed to evaluate the claimed relationship.

Tags

# Autocorrelation and frequency of occurence


# Autocorrelation and frequency of occurence












Recently, I started reading Zuckerman's biography of Jim Simons - "The Man Who Solved the Market". There is an interesting para on page 110 - "When you flip a coin, you have a 25% chance of getting heads twice in a row, but there in correlation b/w one flip to the next. By contrast,Straus, Laufer and Berlekamp determine that the correlation of price moves in deutche marks b/w any two consecutive time periods was as much as 20%, meaning that the sequence repeated more than half the time" - This last line is throwing me off....I've always used autocorrelation, or correlation as is done in traditional statistics courses; just the degree of association b/w two data series at a point in time, or over time etc. I've never associated either of the two metrics to a frequency of an event occurring. I've no idea how the author connects the 20% autocorrelation to the event occurring more than half the time....could anyone elaborate and point me in the right direction? Thanks!

## Answer by vpy (score 1)

https://quant.stackexchange.com/a/53361

I recently had trouble with a similar concept and I managed to develop a proof that related probability of successive occurrence with autocorrelation. Interpreting Autocorrelation as probability. Let me know if it helps.

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.