Lead-Lag Best Lag

Problem

Find the lag that best aligns two equal-length series by absolute Pearson correlation. For lag k >= 0 compare x[0..n-k-1] with y[k..n-1]; for k < 0 compare x[-k..n-1] with y[0..n+k-1]. Search every lag from -max_lag to max_lag.

Return the lag with the largest absolute correlation; ties prefer the lag closest to zero, and at equal distance the negative one. Return None when no lag has at least two paired points.

Hint

Iterate candidate lags in order 0, -1, 1, -2, 2 to settle ties deterministically.

Test cases

case 1

in: [[1,4,9,16,25,36],[0,1,4,9,16,25],2]

expected: 1

case 2

in: [[1,2,3,4,5,6],[20,21,22,23,24,25],2]

expected: 0

case 3

in: [[1,4,9,16,25,36],[4,9,16,25,36,49],2]

expected: -1

case 4

in: [[1,2,3],[3,2,1],2]

expected: 0

case 5

in: [[0,1,3,2,5,4],[1,3,2,5,4,7],2]

expected: -1

Starter codePython

def best_lag(x, y, max_lag):
    # Your code here
    pass

5 test cases · run your code against them in the editor