Cross Correlation Calculator

How it is calculated

For a whole-number lag k the tool pairs xi with yi+k, using only the pairs where both values exist, and then computes the Pearson coefficient on those pairs: r = Σ(x − x̄)(y − ȳ) ÷ √(Σ(x − x̄)² × Σ(y − ȳ)²). A positive lag means Y is delayed relative to X, and a negative lag means Y comes earlier. The number of pairs is shown, and it shrinks as |lag| grows. Enter each series as numbers separated by spaces, commas, semicolons or tabs, with at least 2 values each; any non-numeric item, fewer than 2 pairs, or a series with no variation returns nothing. The lag is rounded to the nearest integer, and a blank lag counts as 0. The result is between −1 and 1 and is shown to four decimals.

Common mistakes

• Using decimal commas such as 2,5. A comma separates values, so 2,5 becomes the two numbers 2 and 5; use a decimal point.
• Reading the sign of the lag backwards. Here a positive lag compares x_i with the later value y_i+k, so it tests whether Y lags behind X, not the reverse.
• Using a large lag on short series. With 8 values and lag 6, only 2 pairs remain and the coefficient is almost always ±1 for no good reason; watch the pairs count.
• Treating high correlation as proof that one series causes the other. It shows they move together after the shift, nothing more.