I have estimated a number of ARCH(p) and GARCH(p,q) specifications - ARCH(1) and GARCH(1,1) specifications to be specific.
Some of them have slightly negative (but statistically insignficant) ARCH coefficients.
Now, I am aware that this implies a misspecification of the conditional variance specification.
Due to the nature of the study, I am limiting myself to ARCH and GARCH specifications and am not estimating IGARCH, EGARCH, etc which would most likely resolve the problem.
My question is therefore:
1) Given that ARCH coefficients are negative but not statistically different from zero, can I accept such a result?
2) How else could I justify these results without needing to change my methodology?
Any ideas and any references?
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