Autocorrelation Calculator

How it is calculated

The tool reads the series (numbers separated by commas, spaces or semicolons), finds the mean x̄, and computes rk = Σ (xt − x̄)(xt−k − x̄) ÷ Σ (xt − x̄)². The numerator sums over the pairs where both values exist (t = k+1 … n); the denominator sums over all n points. Because the denominator always uses the full series, the value is the usual biased sample estimator and shrinks as the lag grows.

The lag must be a whole number from 1 to n−1; a blank lag defaults to 1. A decimal lag, a lag of 0 or one that is too large gives no result. So does a series with fewer than two values, a constant series (zero variance), or any entry that is not a number: nothing is silently dropped.

Common mistakes

• Writing decimals with a comma (2,5) inside the series. The comma is a separator there, so 2,5 is read as the two numbers 2 and 5. Use a point for decimals.
• Leaving a typo such as “abc” in the list. The whole input is rejected and no result appears, so look for the stray token instead of assuming the lag is wrong.
• Expecting a steadily rising series to give a value near 1. With the biased denominator, six evenly rising values give only 0.5 at lag 1, and short series always look weaker at long lags.
• Using a lag equal to or larger than the number of values, a decimal lag, or a lag of 0. None of these gives a result, because there are no pairs left or the lag is not a whole step.
• Reading a high value on a trending series as a repeating cycle. A trend alone produces high autocorrelation, so remove the trend first if you are looking for seasonality.