AR(1) h-Step Forecast

Problem

Compute the h-step-ahead forecast of an AR(1) model with intercept c, autoregressive coefficient phi, and last observed value y_last. For phi not equal to one the closed form is c * (1 - phi^h) / (1 - phi) + phi^h * y_last.

A unit root (phi = 1) requires the separate form y_last + c * h, and a horizon of zero or less returns the last observed value.

Hint

Stationary forecasts decay toward the unconditional mean c / (1 - phi).

Test cases

case 1

in: [0.5,0.5,2,2]

expected: 1.25

case 2

in: [0,0.9,10,3]

expected: 7.29

case 3

in: [1,1,3,4]

expected: 7

case 4

in: [0.5,0.5,2,0]

expected: 2

Starter codePython

def ar1_h_step_forecast(c, phi, y_last, h):
    # Your code here
    pass

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