Return Autocorrelation: Measuring Whether a Recent Move Tends to Continue

Charts can create the impression that rising prices keep rising and falling prices keep falling. You can test that impression numerically by measuring the relationship between the previous return and the next. That correlation is called autocorrelation.

How much does the previous move tell you about the next?

Autocorrelation compares a series with a time-shifted version of itself. For candle returns, pair each return with the preceding candle's return and calculate correlation. A one-step shift gives lag-1 autocorrelation, commonly written ρ1.

The computation is simple: create a return series, shift a copy by one observation and calculate their correlation. A spreadsheet function can do it. The difficult part is interpreting the result, where most misunderstandings occur.

A small sample can easily produce 0.2

The first calculation will usually be nonzero. Values such as 0.13 or −0.09 may look like discoveries, but random data can produce them. The expected noise depends on sample size.

The same −0.05 is weak evidence from 100 bars but may support a reversal tendency from 10,000. Always report how many observations produced the number. The same issue affects win rates; see trade sample size.

A real correlation is useless for trading if it cannot cover costs

Statistical evidence of nonzero correlation is separate from whether its magnitude is economically tradable. A simplified linear model translates it into an expected next-bar move.

Solving ρ1 × 0.4% > 0.10% gives a required ρ1 > 0.25. The original guide argues that a stable 0.25 correlation is extremely difficult to find in liquid major-coin minute or hourly returns, since trading would tend to erode it. See round-trip trading costs for the 0.10% assumption and frequency and fee drag for accumulation.

False negative autocorrelation: Bid-ask bounce

Short-interval returns often show weak negative correlation. This may reflect transactions alternating between bid and ask rather than genuine market reversal: an artifact of recorded execution prices.

Do not accept negative second- or tick-level autocorrelation at face value. Recalculate using the midpoint of bid and ask. If it disappears, the effect came from transaction recording rather than underlying price behavior. See reading the order book.

Timeframes and regimes can reverse the sign

Autocorrelation is not a fixed property of the entire market. It varies with sampling interval and measurement period, sometimes changing sign.

A full-period zero can mean little linear dependence, or opposing regimes masking one another. Separate measurement can reveal more. See market regimes, ADX for trend strength, and mean reversion for the reversal premise.

Measurement procedure: Define the sequence first

A few lines calculate correlation, but the result becomes unreliable without a sound measurement process.

The last item is especially important. Six timeframes × 20 coins × five periods = 600 attempts. Some readings exceeding the noise range are expected by chance, not automatically discoveries. See multiple-testing traps. Check lookahead bias for future-information leakage, walk-forward analysis and the backtesting guide for strategy validation, and overfitting for tuning settings to the data.

Recap

Assess whether the effect exceeds costs, not merely whether correlation exists. A nonzero value alone does not justify a trade. Sample size and round-trip costs make it interpretable.

Caution

All figures are hypothetical illustrations, not observed asset or account measurements: 0.4% standard deviation, 0.05 and 0.25 correlations, 0.10% fees, samples of 100, 1,000 and 10,000 bars, minute/hour/day readings of −0.04/+0.02/+0.06, regime readings of +0.11/−0.08, quotes of 100.00/100.02 and 600 attempts. The 1 ÷ √n approximation assumes independence; clustered market volatility can widen uncertainty. Autocorrelation measures linear relationships only, so zero does not exclude nonlinear dependence. Nonzero historical dependence does not ensure persistence or future profit. Leverage can lose all principal, and decisions remain your responsibility.