Granger Causality F from Series

Problem

Test Granger causality by fitting two OLS regressions on t = 1..n-1: the restricted model y[t] = a + b * y[t-1] and the unrestricted model y[t] = a + b * y[t-1] + c * x[t-1]. Return the F-statistic (SSE_r - SSE_u) / (SSE_u / (m - 3)) with m = n - 1 observations and three unrestricted parameters.

Return 0.0 for fewer than five points, a singular fit, or a perfect unrestricted fit with SSE_u = 0.

Hint

A large F means the lagged x variable explains residual variation that lagged y cannot.

Test cases

case 1

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

expected: 27.867455621301787

case 2

in: [[1,2,3,4,5,6],[0,1,2,3,4,5]]

expected: 0

case 3

in: [[2,3,3,4,4,5,6,7],[1,0,2,1,3,2,4,3]]

expected: 8.34001196172248

case 4

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

expected: 0

Starter codePython

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

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