ADF Lag-One Slope

Problem

Run the core regression of an ADF-style stationarity test by hand. Regress the first difference at time t on the level at time t-1 without an intercept, so the slope is sum(x[t-1] * dx[t]) / sum(x[t-1]^2).

Return 0.0 when there are fewer than two observations or when the denominator is zero. A strongly negative slope is evidence of stationarity.

Hint

The numerator telescopes: it is half of the change in the squared level.

Test cases

case 1

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

expected: 0.42857142857142855

case 2

in: [[0,0,0]]

expected: 0

case 3

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

expected: -0.2

case 4

in: [[5]]

expected: 0

Starter codePython

def adf_lag1_slope(series):
    # Your code here
    pass

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