ADF t-Statistic Lite

Problem

Compute the Dickey-Fuller t-statistic for a series by regressing the first differences on the lagged level with an intercept: dy[t] = a + b * y[t-1]. Return t = b / se(b), where se(b) = sqrt(SSE / ((m - 2) * Sxx)) and m is the number of differences.

Return 0.0 when there are fewer than four observations or the regression is degenerate (zero Sxx or zero standard error).

Hint

A deterministic linear series leaves no residual variance, so the t-statistic is defined as 0.

Test cases

case 1

in: [[1,2,3,4,5,6,7,8]]

expected: 0

case 2

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

expected: -1.6598500055174643

case 3

in: [[1,2,3]]

expected: 0

case 4

in: [[10,11,13,12,15,14,16,17]]

expected: -0.8451542547285166

case 5

in: [[3,1,4,1,5,9,2,6]]

expected: -2.5885640954239317

Starter codePython

def adf_t_statistic(series):
    # Your code here
    pass

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