Dickey-Fuller

Dickey-Fuller

Dickey-Fuller

1-Use augmented Dickey-Fuller tests to determine whether your chosen series is a unit root process. Transform and re-test as appropriate to determine the order of integration. ( 20 mark )

2-Define and estimate the ACF and PACF for your stationary time series (i.e. after differencing your data if appropriate). (10 mark)

3-Select the most appropriate ARIMA time series model for your data on the basis of ACF and PACF plots and appropriate experimentation. (40 mark)

4-Withhold ten per cent of the most recent data and re-estimate two of the equations you estimated in (3). Using the re-estimated equations calculate forecasts (for the withheld data) for each model using Excel. Judge which forecasts are ˜best’ using a criterion such as RMSE (30 mark ).

the Dickey-Fuller test

The Dickey-Fuller test is testing if ϕ=0 in this model of the data:

yt=α+βt+ϕyt−1+et

which is written as

Δyt=yt−yt−1=α+βt+γyt−1+et

where

yt is your data.

It is written this way so we can do a linear regression of Δyt against t and yt−1 and test if γ is different from 0.

If γ=0, then we have a random walk process. If not and −1<1+γ<1, then we have a stationary process.

the augmented Dickey-Fuller test