Integrated Autocorrelation Time

Problem

Estimate the integrated autocorrelation time as tau = 1 + 2 * sum over lags 1..max_lag of the sample autocorrelation at that lag. Each autocorrelation is the sum over i of (x[i] - mean) * (x[i + lag] - mean) divided by the total sum of squared deviations. Return 1.0 for fewer than two samples, max_lag < 1, or a constant sequence.

Hint

Positive autocorrelation inflates the variance of the sample mean, so tau exceeds 1.

Test cases

case 1

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

expected: 1.8

case 2

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

expected: 1.6

case 3

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

expected: 1

case 4

in: [[5],4]

expected: 1

case 5

in: [[1,3,2,4,3],2]

expected: 1.046153846153846

Starter codePython

def integrated_autocorrelation_time(samples, max_lag):
    # Your code here
    pass

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