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I am using the log returns of 3 different stock indices.

Two of them show improvements in AIC/BIC critereon when I fit EGARCH(1,1) in comparison to GARCH(1,1). One does not. Assuming that estimation procedures are identical, what could be a practical or theoretical reason that EGARCH is not an improvement for index 3?

Index 1

GARCH (1,1) AIC -211083.23
GARCH (1,1) BIC -211388.52

EGARCH(1,1) AIC -21426.9 EGARCH(1,1) BIC -21315.3

Index 2

GARCH (1,1) AIC -21748.75
GARCH (1,1) BIC -21893.34

EGARCH(1,1) AIC -22580.85 EGARCH(1,1) BIC -22457.69

Index 3

GARCH (1,1) AIC -22189.38
GARCH (1,1) BIC -22174.91

EGARCH(1,1) AIC -21335.42 EGARCH(1,1) BIC -21606.81

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Theoretical reason: if the true model is GARCH(1,1), then given a large enough sample, AIC and BIC will prefer GARCH(1,1) to EGARCH(1,1) (or to any other model). Of course, we need not assume that the true model is strictly GARCH(1,1); it is enough to assume that the true model is more similar to GARCH(1,1) than to EGARCH(1,1).

In practice that could mean that the third stock index is generated by a different process than the first two indices, where the difference is not only in model coefficients but also in the functional form.

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  • $\begingroup$ I estimated EGARCH(2,1) for the third index and found it to be superior to the GARCH(1,1). What can we conclude from this/our data? $\endgroup$ – Harry May 9 '15 at 13:27

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