garch 1


Is the Arch(1) model better than the GARCH(1,1) model?

  • Interestingly, the best models do not provide a signi?cantly better forecast than the GARCH(1,1) model. This result is estab- lished by the tests for superior predictive ability of White (2000) and Hansen (2001). If an ARCH(1) model is selected as the benchmark, it is clearly outperformed.

Why doesn’t the dsuof White (2000) use the GARCH(1) model?

  • The reason is that the DSuof White (2000) is sensitive to inclusion of poor models, see Hansen (2001). When we use the GARCH(1,1) and the bench- mark model, there are several models that are considerably worse performing relative to the GARCH(1,1).

What is the general form of the earch(1) model?

  • The general form of the EARCH(1) model is It can also be shown that the conditions for stationarity, unlike the GARCH(1,1) model, are thesame for both wide-sense (almost sure) and covariance stationarity. A necessary and sucientcondition for this is <1.
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