ARMA(1,1) One-Step Forecast

Problem

For the ARMA(1,1) model x[t] = c + phi * x[t-1] + e[t] + theta * e[t-1], compute the one-step-ahead forecast conditional on the last observation and the last residual: c + phi * x_last + theta * e_last.

Return the forecast as a number.

Hint

Future innovations have expectation zero, so only the last residual enters.

Test cases

case 1

in: [1,0.5,0.3,10,2]

expected: 6.6

case 2

in: [0,0.8,-0.5,5,1]

expected: 3.5

case 3

in: [2,0,0,7,3]

expected: 2

case 4

in: [1,0.5,0.3,10,0]

expected: 6

Starter codePython

def arma11_forecast(c, phi, theta, x_last, e_last):
    # Your code here
    pass

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