Partial Autocorrelation Lag 1

Problem

Estimate the lag-1 partial autocorrelation as the sample Pearson correlation between the series and itself shifted by one: correlate x[0..n-2] with x[1..n-1], centering each sub-series on its own mean.

Return 0.0 if the series has fewer than three points or either sub-series is constant. For lag 1 this equals the regression-based PACF.

Hint

This is just Pearson correlation between the two overlapping sub-series.

Test cases

case 1

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

expected: 0.9999999999999998

case 2

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

expected: -0.4999999999999999

case 3

in: [[5,5,5,5]]

expected: 0

case 4

in: [[4,2,8,6]]

expected: -0.1428571428571428

Starter codePython

def partial_autocorrelation_lag1(series):
    # Your code here
    pass

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