1. Testing for unit roots in Eviews
Open ‘ukhp.wfl’. We test whether the series of ‘hp’ is unit root.

2. Repeat the above steps to test whether the series of ‘dhp’ is unit root.

3. Testing for cointegration and modelling cointegrated systems using Eviews
To overcome the problems of the spurious regression, we use the difference of series to analysis. However, this methodology will diminish the long-run relationship between the two original series.
The S&P500 spot and futures are cointegrated, this means that the spot and futures prices have a long-term relationship.
𝐹=𝑆 1+𝑟 .

4. The Engle-Granger 2-step method
Open ‘sandphedge.wfl’
Generate a new equation object:
LSPOT C LFUTURES
Generate a new series:
STATRESIDS=RESID
Perform the ADF test on the residual series.

7. Since the test statistic (-8
Since the test statistic (-8.05), the null hypothesis of a unit root in the test regression residuals is strongly rejected.
The two series are cointegrated.
An error correction model (ECM) can be estimated, as there is a linear combination of the spot and futures prices that would be stationary.

8. rspot c rfutures statresids(-1)
STEP 2:
We estimate an error correlation model (ECM) by running the regression:
rspot c rfutures statresids(-1)

9. ARCH
Open ‘currencies.wf1’

11. GARCH
The GARCH model was developed independently by Bollerslev (1986) and Taylor (1986).
𝜎 𝑡 2 is known as the conditional variance.

12. GARCH Quick/Estimate Equation.
Select ARCH from the ‘Estimation Settings’

14. GJR
The GJR (Glosten, Jagannathan, and Runkle, 1993) model is a simple extension of GARCH with an additional term added to account for possible asymmetries.

15. GJR

16. EGARCH
The exponential GARCH model was proposed by Nelson (1991).

17. EGARCH

18. Forecasting from GARCH models
We stopped the estimation of the GARCH(1,1) model for the Japanese yen returns on 6 July 2005 so as to keep the last two years of data for forecasting.

19. Forecasting from GARCH models

20. Dynamic forecast

21. Static forecast