Testing for unit roots in Eviews

• Open ‘ukhp.wfl’. We test whether the series of ‘hp’ is unit root.

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

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.

The Engle-Granger 2-step method

• Step 1:• 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.

• 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.

• STEP 2:We estimate an error correlation model (ECM) by running the regression:

rspot c rfutures statresids(-1)

ARCH

• Open ‘currencies.wf1’

GARCH

• The GARCH model was developed independently by Bollerslev (1986) and Taylor (1986).

• is known as the conditional variance.

GARCH

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

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.

GJR

EGARCH

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

EGARCH

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.

Forecasting from GARCH models

Dynamic forecast

Static forecast