TS Module 15: Forecasting basics HW

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Homework assignment: ARIMA(1,1,0) forecasts

An ARIMA(1,1,0) process has 40 observations y_t, t = 1, 2, …, 40, with y₄₀ = 60 and y₃₉ = 50.

This time series is not stationary, but its first differences are a stationary AR(1) process.

The parameter è₀ of the stationary AR(1) time series of first differences is 5.

The 1 period ahead forecast ŷ₄₀(1) is 60.

We determine the 2 period ahead forecast ŷ₄₀(2).

A.     What is the most recent value of the autoregressive model of first differences? Derive this value from the most recent two values of the ARIMA(1,1,0) process.

B.     What is the one period ahead forecast of the first differences? Derive this value from the the one period ahead forecast of the ARIMA(1,1,0) process.

C.    What is the parameter ö₁ of the AR(1) process of first differences? Derive this parameter from the 1 period ahead forecast.

D.    What is the two periods ahead forecast of the AR(1) process of first differences? Use the parameter of the AR(1) process.

E.     What is the two periods ahead forecast of the ARIMA(1,1,0) process? Derive this from the two periods ahead forecast of the AR(1) process.