Sample Autocorrelation Calculator
Calculate a selected lag autocorrelation using the common global mean and full centered square-sum denominator.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Center every observation by the same global mean and divide the lagged cross-product by the full centered energy.
r(k)=Σᵢ₌ₖ₊₁ⁿ(xᵢ−x̄)(xᵢ₋ₖ−x̄)/Σᵢ₌₁ⁿ(xᵢ−x̄)²
Worked example
For 1,2,3,4,5 at lag one, centered energy is 10 and lagged cross-product is 4, giving r(1)=0.4.
Assumptions and input details
Lag must be below observation count and variance nonzero. This is the biased-denominator descriptive ACF convention, not Pearson correlation of two shortened vectors, an unbiased covariance estimator or a significance test. Equal spacing must be supplied.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Calculate full finite cross correlation and a signed global-energy-normalized absolute peak lag for two numeric sample records.
Calculate the Durbin–Watson residual sequence statistic and lag-one product ratio.
Compare trailing simple moving averages with first-value-seeded exponential smoothing for an ordered series.
Reserved advertising space.