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 in this model of the data:
which is written as
is your data.
It is written this way so we can do a linear regression of against and and test if is different from 0.
If , then we have a random walk process. If not and , then we have a stationary process.