Return Autocorrelation Calculator
Calculate the NIST lag-k autocorrelation of ordered equal-frequency returns, with every paired deviation and the fixed 95% white-noise reference band visible.
Enter ordered equal-frequency returns
Use signed percentage returns from one consistent sampling rule, oldest to newest. Choose a lag from 1 to the supported history boundary.
Enter percentage numbers without percent signs. Separate with spaces, commas, semicolons or new lines. Maximum 500.
Entered return autocorrelation arithmetic
Entered Strategy Diagnostics 1.0.0.
| Pair | Earlier index | Later index | Earlier return | Later return | Earlier deviation | Later deviation | Cross-product |
|---|
How return autocorrelation is calculated
95% white-noise reference = ±1.96 ÷ √N
Version 1.0.0 follows the NIST autocorrelation definition: both lagged members use the mean of all N entered observations, the numerator includes N minus k ordered pairs, and the denominator includes all N squared deviations.
The displayed reference band is the NIST fixed-width approximation for checking white-noise randomness. It is a comparison aid, not a trading threshold or proof that returns are independent.
Assumptions and limits
- Enter 3 to 500 signed percentage returns in oldest-to-newest order.
- Lag must be a whole number from 1 to the smaller of 50 or N minus 2.
- Observations should be equally spaced and use one consistent net-or-gross return convention.
- A constant series is rejected because its autocorrelation denominator is zero.
- No direction, predictability, strategy quality, next-return or recommendation label is produced.
Worked example from the audited fixture
The audited fixture contains 30 ordered percentage returns and uses lag 1. Its full-sample mean is 0.110000%, while the lag calculation contains 29 adjacent pairs.
95% white-noise reference = ±1.96 ÷ √30 = ±0.357845
How to interpret the result
The absolute coefficient, 0.160966, is inside this fixed reference band. The denominator uses all 30 deviations even though the numerator has 29 lagged pairs. This comparison does not establish independence, reversal or the direction of the next return.
Frequently asked questions
- Enter 3 to 500 signed percentage returns in equal-frequency oldest-to-newest order and choose a supported whole-number lag.
- Each of N minus k paired deviations is multiplied and summed, then divided by the squared-deviation sum across all N entered returns.
- Both the earlier and later member of every lagged pair use the mean of all N entered observations.
- Version 1.0.0 follows the published NIST autocorrelation definition, whose denominator is the full-sample squared-deviation sum.
- It is the NIST white-noise comparison approximation plus or minus 1.96 divided by the square root of N.
- The denominator is zero, so autocorrelation is undefined and the calculation is rejected.
- No. This page compares one ordered return series with itself at a lag; the matrix compares two aligned instrument series.
- No. The comparison does not prove causation, stable dependence, persistence, reversal, a signal or future performance.
Sources and methodology
- NIST/SEMATECH — Autocorrelation — Published lag-k numerator, full-sample denominator and equal-spacing assumption.
- NIST/SEMATECH — Autocorrelation Plot — Published fixed 95% white-noise reference-band approximation and its limits.
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