Autocorrelation Calculator

Measure autocorrelation at a given lag and test for serial dependence.

About Autocorrelation Calculator

Autocorrelation measures whether a series is correlated with its own past. Positive serial correlation violates the independence assumption of ordinary regression and understates standard errors. Ignoring autocorrelation in time-series regression produces standard errors that are far too small, making spurious relationships look significant.

Formula

Autocorrelation

r_k = covariance at lag k ÷ variance; significance bound ≈ 1.96 ÷ √n

Durbin-Watson: Approximately 2(1 − r₁); values near 2 indicate no autocorrelation

Worked example

With the default values below, Autocorrelation Calculator returns Autocorrelation at That Lag of 0.600000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Covariance at the chosen lag: 18
Variance of the seriesminimum 0: 30
Number of observationsminimum 4: 120
Lagaccepts 1–100: 1

Results

Autocorrelation at That Lag: 0.600000
Significance Bound: 0.178919
Approximate Durbin-Watson Statistic: 0.80000
Is It Significant: Yes — beyond the significance bound
Interpretation: Positive serial correlation — consecutive values move together

Step by step

1Values used
2Autocorrelation
3Autocorrelation at That Lag= 0.600000
4Significance Bound= 0.178919
5Approximate Durbin-Watson Statistic= 0.80000
6Is It Significant= Yes — beyond the significance bound
7Interpretation= Positive serial correlation — consecutive values move together

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Autocorrelation calculated?

r_k = covariance at lag k ÷ variance; significance bound ≈ 1.96 ÷ √n Autocorrelation measures whether a series is correlated with its own past. Positive serial correlation violates the independence assumption of ordinary regression and understates standard errors.

Why does Autocorrelation matter?

Ignoring autocorrelation in time-series regression produces standard errors that are far too small, making spurious relationships look significant.

What values do I need to enter?

This calculator takes 4 inputs: Covariance at the chosen lag, Variance of the series, Number of observations, Lag. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.